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1 | Timestamp | Last Name | First Name | 1. Explain step by step the process of solving a "linear model" word problem. | 2. What does the word "extrapolating" mean? Give an example. | 3. Write your own linear model word problem. Include all pieces shown in examples. Your problem must include a "backstory" like the examples in the SSS. Be creative in choosing your characters and backstory because your storyline will continue throughout the entire school year as you complete assignments called "WPPs" | 4. Solve step by step (verbally) the problem you wrote in question #3. (This means you explain in words as if you were talking to someone else) | 5. Compare and contrast the two different types of costs we have. Explain in detail. | 6. Explain the difference between revenue and profit. Give an example from real life to support your response. | 7. Write your own Profit-Revenue-Cost word problem. Include all pieces shown in examples. Use the same characters as you did in your previous word problem | 8. Solve step-by-step (verbally) the problem you wrote in #7 above | 9. The most important facts, terms, and tips I need to remember from these three concepts are _________________ | 10. The part I understood the most from these TWO concepts is:_____________ | 11. The part I am still confused about from these TWO concepts is: ___________________ | EMAIL ADDRESS | ||||

2 | 6/20/2012 21:29:02 | 1-ANSWER KEY Kirch | Mrs. | To solve a linear model word problem, you must first identify the coordinates in the problem. The x values will be represented by time, whereas the y value will represent an amount. Once you have the ordered pairs, you just write the equation of the line passing thru those two points using the slope formula no y=mx+b as we did in concept 2. The problem also asks for some other information for different weeks and you just plug in that number for x, like you are evaluating it. | Extrapolating means to look at data in the future assuming the pattern is going to continue. For example, if I only have information for week 1 and week 5, but think that the pattern is going to continue, I can extrapolate that data to predict what will happen in week 9 or another week in the future. | Can't wait to read yours! | Make sure you solved it right! | The two types of costs we have are variable costs and fixed costs. Fixed costs are things that stay the same every month, such as rent,utilities, advertising, etc. variable costs depend on the item you are making and how many you produce or sell that month. The cost function consists of both fixed and variable costs. The fixed is just the number, whereas the variable costs have the variable attached to it. | Revenue is the amount of money you bring in,whereas profit is the amount of money you actually make after paying all your bills. So, for example, if you have a job and bring home a paycheck of $1000, but have to pay your cell phone bill and a few other bills that add up to $200, then your revenue may be $1000, but your profit is only $800. | Can't wait to see your creativity... Make sure the story flows! | Solve it right :) | For you | For me | For me | |||||

3 | 6/25/2013 18:20:36 | Aguirre | Melissa | 1) Read the word problem and highlight any important information. 2)Translate the numbers they give you into two points. For example, if it says that in the first week they sold 6 books, then the point would be (1,6). 3)From those two points you have, look for the slope. 4) From that information, use one of the set of points (preferably the smallest one) and plug it into the y=mx+b form. 5) From that information you should be able to have the equation in f(x)=#x+/- b. 6) If they ask you to find the number of product sold in the 5th week, for example, then just plug in the numbers into the equation that you came up with. | It means to estimate (a value of a variable outside a known range) from values within a known range by assuming that the estimated value follows logically from the known values. So if you were to plot two numbers, you'd need a huge scale. So all the numbers in between would be extrapolated from the two points. You can figure out what's happening all the way to the other end. In the picture that Mrs. Kirch showed us, there was a teacher who asked his student why he didn't do questions 1-20 because the student only did 5,10,15 and 20. The student responded by saying that he was hoping that the teacher would extrapolate the answers from the previous questions. | Ava loves collecting post stamps even though she never sends any postcards. She looks for them when she goes traveling to different countries. When she first started out collecting them, in her first week, she had gotten 10. By the 6th week, she had collected 55 stamps. Assuming her collection follows a linear model, (a) write the linear equation to model the number of stamps collected; (b), calculate how many stamps she would have by the 8th week' and (c) predict how many stamps she would have during week 15 if this pattern continues. | So this problem translates to having the points (1,10) and (6,55). I got these numbers because in the first week she had gotten 10 stamps and on the 6th week she had a total of 55 stamps. Then from those two points you have to find the slope. The slope would be (55-5) =45 and (5-1)=4 so the slope is 9=m. Then you get the formula y=mx+b and plug in (1,10) . The equation would be 10=9(1) + b . B would end up being 1. So the equation you would end up getting would be f(x)=9x+1 (9x coming from the slope and 1 from the b) You would use this equation to plug into the question it's asking you to solve. For finding the number of stamps on the 8th week you would plug into the formula making f(x)= 9(8)+1 =73 stamps. Then for the 15th week you would have f(x)=9(15)+1= 136 stamps. | The two different types of cost we have are fixed costs and variable costs. Fixed costs stay about the same every month, it would be paying for the rent, utilities, advertising ,etc. For variable costs it varies because it depends on how many items you decide to produce. So for one month you can pay 5 dollars for a shirt you make but that doesn't mean you're going to pay 5$ every single month. The equation for cost would be c(x)= (fixed cost)+(variable costs). | Revenue is how much you charge for each item you sell. The equation is r(x)=#x . An example would be that you sell pencils for $1.50 each. Profit is how much you make from your business. You would get the profit by taking your revenues and subtracting the costs, p(x)=r(x)-c(x). Using the pencil example, if it costs you 1400 for monthly equipment and rental fees, and .25 for supplies. The fixed equation would be 1400+.25x. For the variable costs , you sell each pencil for .75 so the equation would be .75x. To get the revenue equation you subtract both of them so it would be .75x-(1400+.25x). Then you distribute the negative and solve so the revenue equation would be .5x-1400. | Ava is starting a stamp selling business. These stamps she collected are from all over the world, so they are really extravagant and foreign. It costs her 1200$ for monthly equipment and rental fee, and 1.50 for the supplies (envelope) that goes along with the stamp. She sells each stamp for 2$ (considering they are ostentatious). Write your (a) cost function; (b) revenue function; (c)profit function; and (d) estimate the number of stamps she has to sell in order to break even (round up). | a) The cost equation is c(x)= 1200+1.50x because it's the rental and the supplies needed. b) The revenue function equation is (r)x= 2x because she is selling the pencils for 2$ each. c) The profit equation is 2x-(1200+1.5x) then you distribute the negative and it comes out to 2x-1200-1.5x= p(x) = .5x-1200. d) To find the break even point you make the equation from the profit equation equal to 0. It would come out to .5x=1200. The answer would be 2400 stamps. e) Finally, to get the profit , you would have to plug in 2400 into the profit equation making .5(2400)-1200 which would equal 0. So Ava would make 0 dollars. | I need to remember how to come up with a linear equation by using word problems. I also need to remember all the types of business problems including: cost (fixed/variable), revenue, profit, and the break even point. I also need to remember the word extrapolate. | I understood both of them because they are fairly easy. | Both of them are understandable. | guagmeli@yahoo.com | ||||

4 | 6/16/2013 22:32:14 | Alfaro | Katherine | How to solve a linear model? Here's how. WARNING: Instructions may be unclear. Step one: In the word problem write down the first number, for example: in the first week(write it down) then write down the following number. Kratos sold 4 samurai swords. Step two: write down the first numbers in this format ( 1, 4 ) Step three: reading on the passage two more numbers will appear and write them down in the same format ( #, # ) Step four: After writing the numbers, we're going to use a formula which is M=Y2-Y1/X2-X1 then plug in the numbers to find the slope. Step five: after finding the slope, you're going to use one of the points and the slope and plug it in the formula of Y=mx+b. to find the y intercept. Step six: The following step it will tell you how much swords did kratos sold in 6 weeks, so you're going to find X and plug in 6. for example 2(6)+1 Step seven: then you're going to predict how much swords kratos sold in 12 weeks and plug in 12 into 2x+1 That's how you solve a linear model. | Extrapolating means: let's say if we plot (7,5) and (9,7) and connect the points, from this point we only know what happened between that specific point, but we don't know what's beyond point (9,7) so we're going to extrapolate it and figure out what's going on beyond that point. | Kratos the god of war of Olympus is collecting gorgon eyes to increase his health. In his first day , he collected 2 gorgon eyes . By the third day he collected four gorgon eyes. Assuming his collecting follows a linear model, A) write the linear equation to model his gorgon eye collection: B) calculate how many gorgon eyes Kratos had in the second day. C) predict how many gorgon eyes will Kratos have in his 6th day if this pattern continues. | First step :I have to write down the numbers it gives us (1,2) and (3,4) second step: we need to put in a formula to find the slope M= 4-2/3-1=2/2=1 Third step : I need to plug it in in Y=mx+b and choose one of the points. 2=1(1)+b=1 y= 1x+1 fourth step: I need to calculate how many gorgon eyes he had in the second day so I need to plug in 2 into the x y=1(2)+1=3 gorgon eyes fifth step: I need to predict how many gorgon eyes will Kratos have in his 6th step and plug in 6 into x again. y=1(6)+1= 5 gorgon eyes. | The two different costs we have are fixed costs and variable costs, Fixed costs is what you pay for each month like electricity, gas, rent and etc. Variable cost is how much you have to pay for to make each item and how much you need to produce. | Revenue is how much you make from an item and how much you charge for it, for example like sales, income and fees earned. Profit is the expense and cost deducted from all the sales and example is the money you get back or earn. | Kratos is starting a business of red orbs to power up weapons. It costs him $1200 for monthly equipment and rental fees, and $2 for supplies for each weapon. He sells each orb for $4. A)write cost function B) Revenue function C)Profit function and D) estimate the number of red orbs he will have to sell to break even. | Step one: Write out the first two numbers the monthly fees and how much for supplies A)c(x)= 1200+2x step two :B) find the revenue, how much he charges for each orb R(x)=4x step three: find the profit function and write It down like this P(x)=4x-(1200+2x) then distribute the negative sign to the numbers inside the parenthesis and combine like terms which will equal to 2x-1200 step four: D=p(x)=2x-1200=0 (equal it to zero and add 1200 to both sides 2x-1200=0 1200 1200 2x=1200 (divide 2x to both sides) 2 2 which equals to 600 red orbs and exact BEP | the definition to business problems. | The linear problem I thought it was pretty easy and I understood it. Word problem are actually not that hard. I think I might just like them. | Is the business problems where I have to find the Break even point I got stuck a little. | kathykratos@yahoo.com | ||||

5 | 6/28/2013 9:38:53 | Alfaro | Ana | to solve a linear model you must first set up two sets of ordered pairs. When you have evaluated x being the time and y being the amount you find the slope of those two points. Once you have found the slope you plug it in to y=mx+b and find out what the y intercept is for this linear model. Once you have completely found the equation you can now plug in any numbers that they are asking you for to extrapolate this line. | extrapolating means to extend which in this case would be an extent of the two ordered pairs that were given to you. For example (1,3) and (2, 4) you find the slope of that which is 1 and use the equation y=mx+b to find the y value and now you can find any value beyond the values that were originally given to us. | Alejandra has decided to start a cookie business since a lot of her friends have told her that her cookies were the best. At first she was not so sure of launching herself in the cookie industry but she finally did. On the first week of her cookie business she sold 24 cookies. On the 5th week she sold 72 cookies. Assuming that her business follows a linear model a)what is the linear equation of this business b)how many cookies did she sell on her 3rd week c) how many cookies will she sell in the 9th week? | we are given that on the first week she sold 24 which is our first set of ordered pairs (1,24) it also gives us that she sold 72 cookies on the 5th week (5,72). we now find the slope of these two points. which would result in being 12. now you plug in the slope into the equation of y=mx+b to find the y-intercept. the equation will end up being a)y=12x+12 b) when you plug in 3 to x you get 48 c) when you plug in 9 you get 120 cookies. | there are two different cost that we have which are fixed cost and variable cost. Fixed cost is constant and does not change while variable cost is the how much it cost to make each items which varies depending in the amount that is made each time. | Revenue is how you sell the item for. Profit is when you subtract your revenue minus your cost leaving you with what you get out of your sell the amount of money that is left untouched. For example a cookie could be sold for the price of 2 dollars which is the revenue. however is make take 75 cents to make each cookie which is your cost. when you subtact your revenue minus your cost you eand up getting you profit which in this case is $1.25. | Alejandra has a monthly fee of $120 for all the equipment she must use. It cost her seventy-five cents to make each cookie and she sells them each for two dollars. What is a) your cost function b) your revenue function c) your profit function and d) the amount of cookies that she must sell n order to get to her breakpoint. | 120 is our fixed cost since it does not change while .75 is our variable because it can change depending on the amount. a) y=120+.75x You sell each item for $2 that the revenue function is b) R(x)= 2x your profit is solved subtracting the revenue minus the cost that it takes to make it which would be P(x)=2x-(120+.75x) when you simplify you get c) y=1.25x-120 your break even point would be when you set all this equal to zero and end up getting 96 which means she has to sell d) 96 cookies to reach her breakeven point. | I must remember that x = time and y= amount. That when we are solving for a linear model we must find the slope of those two points in order to find the next points. Know that fixed cost is constant and doesn't change while variable cost changes depending on how many you make the amount. Revenue is how much you charge for that specific item and profit is the revenue minus the cost it took you to make it. Also, that the break even point is when you don't gain or loose money. | the part I understood the most of these two concepts was how to solve the equation for a linear model since it was easy for me to identify the ordered pairs and go from there. | I am not confused with anything at the moment having to do with these two concepts. | anaalfaro1997@gmail.com | ||||

6 | 6/24/2013 23:31:41 | Alvarado | Cynthia | You first find the points that are going to be plotted on the graph. Then, you find the slope and once you've found it you plug any point with the slope into y= mx+b and then you get your equation. After, you plug in any number they are asking you to solve for. | To assume. When you are only given the points of the progress of week 1 and 6 of something assuming that its going at the same rate. | Luke loves buying shirts. During week 1 he had bought 5 shirts. By the sixth week had had bought 50 shirts. Assuming his purchases follow a linear model (a) write the linear equation to model his purchases of shirts; (b) calculate how many shirts Luke had bought during week 3; and (c) calculate how many shirts Luke will have by week 9 if this pattern continues. | The first two points that would be on the graph you be (1,5) and (6,50). You subtract 50-5 and 6-1. You get 45/5 and simplify it to 9, therefore your slope is 9. You choose a point to plug into y= mx+b. 5= (9)(1)+b. You subtract 9 to both sides and get -4=b. Therefore you equation is f(x)= 9x-4. To find how many shirts Luke had during week 3 you plug in 3 into the equation. f(3)= 9(3)-4. 27-4=23. So Luke had 23 shirts by week 3. To find how many he will have by week 9 you plug 9 in. f(9)= 9(9)-4. 81-4= 77. Luke will have 77 shirts by week 9. | The two different types of costs that we have are fixed costs and variable costs. Fixed costs is what you pay monthly and it stays the same. Variable costs is how much it costs to make each item and it's never the same. | Revenue is how much you charge for each item that you sell. Profit is when you take your revenue and subtract your costs. If you charge $2 for an ice cream you would subtract $2 from all your costs. | Calum is starting a bracelet business. It costs him $2400 for monthly equipment and rental fees, and $.50 for supplies for each bracelet. He sells each bracelet for $1.50. Write his (a) cost function; (b) revenue function; (c) profit function; and (d) estimate the number of bracelets that Calum will have to sell in order to break even (round up to the nearest bracelet if necessary and tell how much profit you will make if you have to round up). | (a) Costs (x)= 2400+.50x (b) Revenue (x)= 1.50x (c) Profit (x)= 1.50x-(2400+.50x). You distribute the negative so your equation will end up being 1x-2400=0. Then you add 2400 to each side and end up with 1x=2400. You then divide each side by 1 and get x=2400. So Calum will have to sell 2400 bracelets to break even. To find the profit you plug in 2400 to 1(2400)-2400. You then get the answer of 0, so Calum doesn't make any profit. | The important tip that I need to remember is when trying to find the profit to think of PRICE because the equation to find profit is P(x)= R(x)-C(x). | How to write linear models and evaluating words problems. | Writing the different costs with the revenue and the profit. | alvarado.cynthia09@yahoo.com | ||||

7 | 6/29/2013 0:36:35 | Alvarez | Connie | This is the process to solving a ''linear model'' word problem, first one has to know that the x-value will always represent time and the y-value will always represent amount. Second, one has to set up two sets of ordered pairs, for example this translates to (week#(time), amount) in order to continue with the problem. Third,in part a one needs to have a linear equation using the numbers from the ordered pair in order to get this equation one needs to find the slope, first use the form of m= y2-y1/x2-x1 to find slope then use the form y=mx+b to finalize step three. Fourth, parts b and c are just plugging in and simplifying. One can get the numbers to plug in from the the word problem, they need to to be plugged in to the linear model one got in part a. | The word extrapolating means to guess or estimate beyond the problem that is already known for example if one is given a set of points to plot on a graph and one wants to keep investigating then its extrapolating. Help??? | 3. Jennifer collects stones from national parks on the weekends. During week 1, she finds 5 stones to start her collection. During week 11, she finds enough of fascinating stones to make her total collection 37 stones. Assuming her findings follow a linear model, (a) Write the linear equation to model her stone collection; (b) calculate how many stones Jennifer had in her collection during week 6; and (c) predict how many stones she will have during week 26 if this pattern continues. | First, you have to arrange two sets of ordered pairs by putting all x-values with time (weeks) and all the y-values with amount (stones), so (1,5),(11,37). Second, you have to put it in a linear equation so you have to find the slope by using the form m= y2-y1/x2-x1, so m=37-5/11-1=32/10=3.2. Third you have to use the form y=mx+b to finalize step three, so lets use ordered pair (1,5), so 5=(3.2)(1)+b becomes b=1.8. Fourth, put it in a linear equation so f(x)=3.2x+18, part a is finished, moving on to part b. Fifth, in part b its asking to find the amount on week 6, so plug in (6) to the linear equations, so f(6)=3.2(6)+18=37.2, so Jennifer sold 37.2 stones in week 6. Sixth, in part c its asking to find the amount on week 26, so plug in (26) to the linear equation, so f(26)=3.2(26)+18=101.2, so Jennifer sold 101.2 stones in week 26. | The difference between the two costs is that they add up to be a decimal and they end up with .2 but, also they is a big gap between them because in 20 weeks she made 64 stones (101.2---37.2)(subtract). It s hard to explain the comparison, they just don't add up. The contrast is that the amount in week 6 has the same amount as in week 11, which is not supposed to be. Help??? | A revenue is the money that is brought in from the product price in contrast profit is the money that is left over after paying everything else like the bills, so you receive the profits. For example, a revenue would be when you receive $80 from a customer who bought $80 pair of Jordan's because thats how much you charged for it, a revenue is like a cashier. For example a profit would be when you own your own business and its the end of the week, its time to pay the electricity, water, etc. so whatever money is left, that is the profit. | Jennifer is starting a stone selling business. (These stones come great national parks like Sequoia National Park and Yosemite National Park.) It costs Jennifer $1500 for monthly equipment and rental fees, and $.75 for supplies for each stone. Jennifer sells each stone for $3. Jennifer will find (a) Cost Function; (b) Revenue Function; (c) Profit Function; and (d) estimate the number of stones that Jennifer will have to sell in order to break even (round up to the nearest stone if necessary and find the amount of profit if you do round up.) | First, one has to find part (a ) costs: the fixed and the variable, so in this case the fixed is $1500 and the variable is $.75, then write them in a equation so C(x)= 1500+.75x. Second, one has to find part (b) revenue: R(x)=3x . Third, one has to find part (c) profit: to find the profit = (3x)-(1500+.75x) then subtract .75x to the other side (3x) to get the profit which will come out to be P(x)= 2.25x-1500 . Fifth, is to find the break-even profit: 0=2.25x-1500, then add 1500 to the other side (0) which will be 1500=2.25x then divide 2.25 to both sides, so it will come out to be 666.66, its BEP is 667 stones. Sixth, is to find the small profit, one has to plug in 667 to 2.25x-1500, so 2.25(667)-1500=$.75 . | I need to remember that in linear models the x-values are time and in y-values are amount, also the term extrapolate which to estimate the ongoing of a problem that is already known. I also need to remember what cost, revenue, profit, break-even point (BEP) represent and how to find them. | I understood concept because all it was to write an equation then plug in and simplify, very simple. | I had difficulty on concept 7 because it asked for four different answers, but the most struggling part was finding the correct numbers for the cost, but the more practice I got the easier it got to solve the four parts. | alvarezconnie63@yahoo.com | ||||

8 | 8/26/2013 17:43:35 | Aranda | Brianna | First you find the slope, then you plug it into y=mx+b with one of the points you found, then you plug in the time they give you such as, f(x). | It means to keep going. For example if you make 8 dollars an hour, a chart only shows how much you have made for 3 hours. Extrapolating means to try and figure out how much you would have by 10 hours. | Ray loves collecting basketball cards. During week 1, he bought a packet of 4 basketball cards. During week 6, he had 34 basketball cards. Assuming his collection follow a linear model. (A) write the linear equation to model his basketball cards collection. (B) calculate how many basketball cards he would have during week 3; and (c) predict how many basketball cards he would have collected by week 21 if this pattern continues. | First you put the time and amount into points: (1,4) and (6,34). Then you do A, by finding the slope of the two points, then plugging it into y=mx+b. then you do B, by plugging in f(3) into the equation. Then you do C, which is the same thing as B, but a different week,and it would be the 21st week, so it would be f(21) and you also plug that into the equation from before. | There is fixed cost and variable cost. Fixed cost is the monthly equipment and rental fees. Variable cost always has a variable, and it is for supplies for anything you are selling. | Revenue is how much you charge for each item you sell. Profit is when you take your revenues and subtract your costs. Example: you sell a frame for 11$ and that would be your revenue. And Profit is when you subtract your costs of frames. | Ray is starting a clothing business. It costs him 1500 for monthly equipment and rental fees, and $3.25 for supplies for each t-shirt. He sells each t-shirt for $14. Write his (a) cost function; (b) revenue function; (c) profit function; and (d) estimate the number of t-shirts he will have to sell in order to break even. | First you get the costs (fixed costs + variable costs(x). Then you do the revenue function and then the profit. Then, you get the break-even point. | I need to remember what cost, revenue, profit, and break-even means. Also that x-value will always represent time. And the y-value will always represent an amount. | Writing linear models and evaluating for word problems. | I a, not confused in any of the two concepts. | briannaaranda90@yahoo.com | ||||

9 | 8/8/2013 18:02:37 | arciniega | bryan | First you find the slope intercept form of the two given pairs, wich would be (time, amount). Once you find the slope intercept form you can plug in other “time” values to give you the “amount” | The word extrapolate means to assume that the linear model is going to continue its pattern. For example if we have to ordered pairs (1,3) (2,6) we can extrapolate what is going to happen the next week which would be (3,9). | Jimmy is a bike enthusiast, so much so that he decided to start a bike shop to sell his favorite custom bikes. At first people didn’t catch on to his style so he only sold 7 bikes his first month. But, by the 6th month he had sold 67 bikes. Assuming his sales follow a linear model, (a) write a linear equation to model his sales; (b) calculate how many bikes he sold the 3rd month; (c) predict how many bikes he will sell in his first year if the pattern continues. | First, you make two ordered pairs of the bikes he sold in his first month and the bikes he sold his 6th month, (1, 7) (6, 67). Once you have these ordered pairs you find there slope and solve for “b” to find the slope intercept form, y= 12x-6. Once you have the slope intercepts form you can plug in the x value to give you how many bikes he sold the 3rd month, (3, 30), and how many bikes he sold in his first year, (12,138). | There are two different types of cost, we have fixed cost, and variable costs. Fixed costs are utilities or things that you play monthly, variable costs are vary depending on how much items you produce. | There is a big difference between revenue and profit, lets say you bought a used car for $2000 and you spend another $2000 on a new paint job, new wheels, and new engine. Then someone likes your car and offers you $5000 dollars for the car so you sell it. Your revenue comes out to a whopping $5000, however your profit is only $1000. So revenue = income and profit = extra earnings. | Jimmy started a custom bike shop business. It cost him 3000, for monthly rent and advertisement, and $150 for supplies for each bike. He sells each bike for $300, write you Cost Function, Revenue Function, Profit Function and estimate how many bikes he must sell to break even. | First you find the cost, c(x)= $3000+$150(x) and the revenue function is r(x)= 300(x), so the profit function would be p(x)= 300(x) – ($3000+$150(x)) which would be p(x)=150(x)-$3000. To find the BEP set p(x)=0. This would be 3000=150(x), which would be 20 so the amount of bikes jimmy needs to sell to break even is 20 | the most important facts and terms that i need to remember is that the break even point is when a business is not making money and not loosing money. also that to find the BEP you need to round to the closest number. | The part i under stood the most is that there is fixed costs that is monthly rent or advertisement and variable costs which vary on how many items you will produce | The part i am still confused about is how to figure out the profit when you round the break even point. | arciniegabryan@yahoo.com | ||||

10 | 8/18/2013 0:51:47 | Arias | Melissa | The first step you have to do is find the x-values that represent time and then find the y-values that represent an amount. You will then have two sets of ordered pairs. After this, you will plug these numbers into the slope formula. Once you have the slope, then pick an ordered pair and plug it into the slope-intercept form. Once solved, you will get an equation made from the slope and the number found after doing the slope-intercep form. After this, you will need to look for the numbers it asks you to calculate in the word problem. For example, calculate how many books Lisa has read during week 2 <--- and predict how many books she has read by week 32 <---. You will need to plug these numbers into the equation you made earlier. When all of this is completed, you will be finished. | If we were to plot the two points given from the linear model, we would extrapolate the rest of the line assuming it followed a linear model. It kind of means to estimate the rest of the line. For example, if we had the points (2,9) and (5,12) we would plot them in a graph and then continue the line by extrapolating it. (assuming it followed a linear model). | Sasha loves to bake and has recently opened up her own cute little bakery. During week one, she sells 10 cakes. During week 6 she is gaining popularity and has sold a total amount of 70 cakes. Assuming her sales follow a linear model, (a) write a linear equation to model her cake sales; (b) calculate how many cakes Sasha had sold during week 3; and (c) predict how many cakes she will have sold during week 52 if this patern continues. | First, the ordered pairs for this problem would be (1,10) and (6,70). Then, plug these numbers into the slope formula. After solving, you will find out that the slope is 12. Plug the slope into the slope-intercept form. Choose an ordered pair to plug into the slope-intercept form as well (Preferably (1,10) because it is easier to do since the numbers are smaller). Once you solve for this, you will find that the answer is -2. Your equation will then be y=12x-2 because of the slope and the number you just found. To find how many cakes Sasha had sold in week 3, plug in 3 to the equation. The answer will be 34 cakes. Finally, to find how many cakes she will sell by week 52, plug in 52 to the equation. The answer will be 622 cakes. | The types of costs that we have are fixed costs and variable costs. Fixed costs stay about the same each month, meaning you know what the rent, supplies, etc. cost. Varied costs vary depending on how much it costs to make each item. It is based on how many items you produce. Varied and Fixed are similar because you have to pay these costs monthly. | Revenue is the money you actually bring in. It is how much you charge for every item that you sell. Profit is the money that you make. To get your profit, you need to subtract your revenues from your costs. For example, all of your costs are $100 and your cost for your item is $10, which is known as your revenue. You need to sell 10 items to pay your costs. Anything more that you sell would be the profit. | Sasha has opened her own small bakery. It costs her $1500 for monthly equipment and rental fees, and $3 for supplies for each cake. She sells each cake for $50. Write her (a) Cost Function; (b) Revenue Function, (c) Profit Function; and (d) estimate the number of cakes she will have to sell in order to break even (round up to the nearest cake if necessary and find the amount of profit if you do round up.) | First, you need to find the Cost Function, Revenue Function, and Profit Function. The Cost Function is C(x)=1500 =3x. The Revenue Function is R(x)= 50x. The Profit Function is P(x)= 47x-1500. Then, you need to equal the Profit Function to 0. You add 1500 to 0 and then divide it by 47. The answer will be 31.9, but since you round, it needs to be 32. To find the profit, you need to plug in 32 to the Profit Function. The profit is $4. | I need to remember all of the facts of revenues and profits in order to not get them confused. For Linear models, I should remember that the x-value represents time and the y-value represents an amount. Terms I should remember are Linear models, Cost Function, Revenue Function, and Profit Function. Tips I need to remember are to read the word problems carefully so I won't get mixed up. | The part I understood most from the linear model was putting an ordered pair into the slope formula to get the slope. The part I most understood from the second concept was finding the Cost Function, Revenue Function, and Profit Function. | I am not confused with anything from these two concepts. | melissa.arias03@yahoo.com | ||||

11 | 8/21/2013 22:41:37 | Av | Molinda | The first step is to figure out the slope by taking the both Ys and Xs and subtracting them. After getting the m value, you need to take one of the order pairs and plugging it to get the equation. After getting the equation, you need to solve for the problems by taking the x value, that represent time, and plugging it to the equation and simplify to get the answers. | Extrapolating is the prediction of the patterns. For example, if we want to figure out how many books Mary will sell in the future, or in a few months, we need to etrapolate the problems. | Jessica and Christine are not only best friend, but they also share a passion for fashion. Because they love fashion so much, they decided to open a fashion store where every one can get the latest fashion. What's unique about the fashion store is that every items of clothing costs $15. During the first week of grand opening, they sold 35 pieces of clothing. By the 7 week, they sold 287 pices of clothing. Assuming their sales follows a linear problems, (a) write the linear equation to model the number of clothing they have sold; (b) calculate how many clothing Jessica and Christine sold during week 4 and (c) predict how many clothing they will sell during week 24. | First of all, you have to determine the x's and y's value. The x represent the week number while the y represent the amount. Starting with the first pair, the x value is 1 because it is the first week. The y value of the first pair is 35 because they sold 35 pieces of clothing. The next order pair is (7,287) because it represent the week and amount. We take the second y minus the first y over the second x minus the first y to determine the slope. The slope would be 42.We take one of the order pair and plug it in to the y=mx+b. My equation end up being y=42x-7.After that, you use the equation to determine how many clothing have been sold by substituting the x. In week 4, Jessica and Christine would sell 161 clothing and by week 24 they would sell 1001 pieces. | The two types are fixed cost and variable cost. The fixed cost is the amount that you pay monthly and are usually the same everymonth. On the other hand, variable cost varies on different items. | The revenue is the amount/ how much something cost. For example, if a customer is a buying a pair of jean that cost $70, then it is the revenue that you are bringing in for your business. While the profit is the actual money that you making from the jeans. If the jean is sold for $70 and it cost you to make only $30, then you're profit is $40. | From the beginning, it cost Jessica and Christine $3000 for monthly rental fees and electricity, and $4 to make each pieces. Jessica and Christine sells it for $15 per clothing. Write your (a) cost function; (b) revenue function; (c) profit function; and (d) estimate the number of clothing they will have to sell in order to break even. | First, the cost function is consist of a fixed and faviarable cost. The cost is fixed cost ($3000) plus the variable cost ($4). The equation should look like C(x)=3000+4. The revenue is the money the item is sold for, which is R(x)=15x. Next, the profit is revenue minux the whole cost function. It should be P(x)=9x-3000. To break even, you add 3000 to the other side and devide by 9. As you a result, Jessica and Christine needs to sell 333 pieces of clothing in order to break even. | When writing linear models, the x value represent time and the y value represent the amount. | To write an equation, you need to solve for the slope by subtracting the second y's with the first y over the second x minus the first x. | none | avmolinda@ymail.com | ||||

12 | 8/22/2013 19:11:00 | Balanzar | Joel | First you must identify the two sets of ordered pairs using time as the x-value and amount as the y-value. | The definition is sort of an educated guess as in that there is information known prior to the guess. One such way would be to draw a scale model of a graph by precise drawing and then acquiring the points by locating them on the graph. | Mr. Balanzar works as a waiter in a restaurant. He earns $1200 per month as a base salary, plus tips averaging 20% of the meals he serves. Write a linear model for the situation, and use it to find the amount earned if Mr. Balanzar serves meals worth a total of $4000. | Step 1: Establish a relation between Mr. Balanzar's total monthly pay and the value of the meals he serves. Monthly pay = Base pay + Tips Monthly pay = Base pay + ((20%)x (value of the meals served)). Step 2: Assigning the labels, we get: Value of the meals served = x Monthly pay in dollars = y Base pay = $1200. Step 3: Forming the equation using the verbal model and the labels, we get: y = 1200 + (20/100)x y = 1200 + 0.2x Thus the linear model that gives the total monthly pay, y, in terms of the value of the meals he serves, x, is y = 0.2x + 1200. Step 4: Substitute x = 4000. y= 0.2(4000) + 1200 y = 800 + 1200 y = 2000. | Fixed costs are paid in a steady rate with an example being something like rent, car payments, and are typically monthly. Variable costs are costs to make a product and varies on amount of items are produced. | Revenue is the amount charged per product for the estimated total amount of money made but profit is that money subtracted by the total costs of the product, one such example would be selling hotdogs for 3 dollars and selling 100 hotdogs to make a total of $300 dollars, however the total costs of the buns and the weiner was 1 dollar and 50 cents to subtract from the revenue and make a total $150 dollars in profit. | You decide to start your eraser selling business. It costs you $1500 for monthly equipment and rental fees and $.50 cents for each eraser box. Erasers are sold for $.75. | The first step in solving this would be addressing fixed and variable costs so the Fixed would be $1500 and the Variable would be $.50. The equation would look like C(x)=$1500+$.50x. After this is done, the revenue must be defined which is $.75 for each eraser, R(x)=$.75 and then the equation for solving profit must be made which is P(x)=$.75x-(1500+.50x) after which you distribute the negative sign and $.75x and add like terms and should end up with P(x)=.25x-1500. The final step is to solve for the Break-Even Point by setting the equation equal to zero and adding 1500 to both sides, then diving 1500 by .25x and solve for the amount of erasers needed to break even. The amount of erasers should end up being 6000. | Cost, Revenue, and Profit. | the making and solving of business problems and linear models. | I am comfortable with this unit and don't need further help. | joel.balanzar@yahoo.com | ||||

13 | 6/27/2013 21:18:14 | Barroso | Gisela | To solve a linear model, is firs underline the week and the other objecmentioned. After you identify your two ordered pairs, you use (y2-y1)/(x2-x1) to find slope to form a linear equation. Then calculate how many objects mentioned will be left in the mentioned weeks, you do this by pluging the number of weeks to the linear equation and then you solve. Andfinally you predict the amount of objects there will be in the next amount of weeks, also by plugging in the amount of weeks into the original linear equation. | It means to predict the next set of a sequence. Meaning that if we're trying to.find the 52 week of how many books Mary sold, we would have to plug in 52 to the linear equation and solve. | Maria is in charge of making new clothing designs. On the first week, she makes 5 new dresses. By the 6th week, she made 30 dresses. Assuming that this is a linear model,(a) write a linear equation to model her total amount of dresses;(b) calculate how many dresses Maria will make by the 12th week;(c) predict how many dresses Maria will make on the 30th week, if this pattern continues. | The first ordered pair will be (1,5) and second ordered pair would be (6,30). Then i would solve for the slope, which would be equal to 5, and then i would plug in the first ordered pair to make a linear equation,which would be y=5X+0. Then i will plug in the number 12 to x on the linear equation and solve, which would equal 60 dresses. And finally i would plug in 30 to x on the linear equation to predict the number of dresses that maria made, whixh would be 150 dresses. | First type of cost is fixed cost, which is when you pay a monthly rate, it will be the same; paying rent,etc. And there is also the variable cost, which is how much it costs to make each item; cost varies monthly based onthe amount of items produced. | Revenue is how much you charge an item, like at a restaurant. And profit.is how much you make which is when you subtract your revenues to your costs, which would be what you made after paying taxes. | Maria has started an alteration business. It costs her $2200 monthly for equipment and rental fees, and $1.50 for each fabric she buys. If she sold each dress for $20. Write(a) cost function;(b) revenue function;(c) profit function ; and (d) estimate the number of dresses Maria will have to sell in order to break even. | First i will underline the given cost ,supplies,revenue,and profit. Then i would set up the cost equation which will be c(x)=2200+1.50x. Revenue is 20x. And profit is p(x)=20x-(2200+1.50x). Profit would then equal 119. And the BEP is $1.50. | Cost ,profit, revenue,break even point,and linear model. | I mostly understood the part where i have to set up a linear model and how to evaluate it. | I am still confused on how to find the break even point of a cost. | bluelkver1416@hotmail.com | ||||

14 | 7/9/2013 10:39:00 | Beas | Metztli | Linear model word problems have two ordered pairs. The x represents time while the y represents the amount of something. You solve by plugging the two into y2-y1 over x2-x1. Once you solve and reduce, the number you get is the slope (m). Next you use one of the t wo ordered pairs to set up a problem. y=mx+b. Plug in the x, y, and slope. All that's left is to solve for b, and when you do, you also plug b in and there's your word problem. | When you assume the problem follows a linear model, extrapolating means you continue the line further than the points given to figure out further quantities. An example would be if you wanted to figure out how many books Mary sold a year after publishing, when you are given data only from the first week and the fifth week. you do this by pugging 52 (the number of weeks in a year) into the x value. | Herbert has kind of been obsessed with stamps since he was a little boy. However only recently has he had the money to start collecting vintage stamps on his own. We think his stamp collecting may become a problem. In the first week he bought five stamps. But by the seventh week Herbert had bought 47 stamps. Assuming his figures follow a linear model, a) write the linear equation to total how many vintage stamps he's bought, b) calculate how many stamps Herbert bought by the fourth week, and c) predict how many this guy's collected in a whole year, 52 weeks. | You have to find the two sets of ordered pairs in the problems: so the first week and the number of stamps collected in it represent the first x and y pair, respectively. Then you see that the information for week seven, with 47 stamps, represents the second ordered pair. You next plug them into y2-y1 over x2-x1 format and get (47-5 / 7-1 .) After we simplify, this gets you 7. The seven is our slope; now choose an ordered pair to plug into the y=mx+b format. We'll use (1,5) to get 5=7(1)+b. solve for b and you get -2. Lastly, you just rewrite the problem to include all the variables. So the solved linear problem is y=7x-2. | There are fixed costs and there are variable costs. Fixed costs are steady and they do not change each month while variable costs VARY, like their name implies. Variable costs are based on how many items are produced and is actually how much it costs to make the item. When combined, they represent cost function, c(x). | Revenue the amount you decide to charge per item you sell, while profit is actually when you have to subtract the cost of items from revenue. An example would be selling lemonade at a stand. If you sold each glass for a dollar, and made twenty dollars, that would be your revenue. But to find out profit, you have to take into account that it cost you about twenty five cents to make each glass. now you have to subtract your costs to find out your actual profit. :) | Okay so Herbert also sells vintage stamps at his day job, a stand at the swapmeet! It costs him fifty dollars monthly to set up shop at that lot, and each stamp was originally bought at thirty cents. However Herb here sells these little treasures for two dollars each. Write your a) cost function, b) profit function, and c) profit function. Then d) estimate how many vintage stamps he needs to sell to break even. | Letter A! Fixed costs are the monthly fees plus how much each stamp cost him. So c(x)= 50+.3X. B) Revenue function is how much he sells each stamp for. R(x)=2x. C is finding profit function. You find this by subtracting cost from revenue. 2x-(50+.3x) is actually 1.7x-50. D) to find BEP you have to set this to zero and simplify. The answer is 29.4 but you round up to 30. So in order to break even HErbert has to sells 30 stamps! | Extrapolate is important to remember. Also, in conceot 7, you have to know the difference between fixed costs and variable costs; and know revenue, profit, and break even point. | I most understood were the business problems. | I am not confused about anything. | metztlibeas@gmail.com | ||||

15 | 8/23/2013 13:57:05 | Beltran | Samuel | Write down (time, amount) of the problem in a set of ordered pairs. Then find the slope and plug it in to find b. This will give you an equation for the problem. | It's when you put the ordered pairs on a graph and assume what happened in between or what can happen in the future. | Little Joel was going by the streets to collect marbles for him to play with. In his first week, he was able to collect 4 marbles. On his tenth week, he had 85 marbles in total. | First you write (1,4) and (10,85). then you find the slope 85-4 / 10-1 = m=9 y=9x + b. then plug in one of the pairs to the equation (4)= 9(1) + b b= -5 f(x)= 9x - 5 | 1) Fixed costs- is a payment that does not change throughout time 2) Variable costs- is the amount of cost to make an item and is followed by X in order to find cost C(x)= fixed costs + (variable costs)(x) | Revenue is how much one charges for an item while PROFIT is the amount of money that one makes- Revenue(x) - Cost(x) | Little Joel started to sell lemonade at his backyard to buy his own marbles. He needs to pay his dad 5 dollars for allowing him to sell lemonade and skip his house chores and it costs $0.10 for every lemon. He sells every lemonade for $0.75. Find Cost Function, Revenue Function, Profit Function, and the Break-Even Point. | His costs equals the fixed cost $5 + variable costs $0.10= 5 + 0.1X= C(x) Revenue is the price he sells for- R(x) = .75X Profit= R(x) - C(x) .75X - (5 + 0.1X) = P(x)= 0.65X - 5 set up P(x) equal to 0 to find BE point 0.65x = 5 /0.65 /0.65 X= 8 lemonades | Break-Even Point and Cost | Linear Models | Pretty good | beltran_samuel19@yahoo.com | ||||

16 | 8/14/2013 19:27:16 | Borroel | Jonathan | First, you must solve for the slope by using the slope formula on the two points given (time is x and amount is y). Next, plug in the slope (m) and one of the two ordered pairs (x and y variables) given into the equation y=mx+b (slope-intercept form) to find the b (y-intercept). Now just plug in the slope and y-intercept and you should have the function necessary to predict other points in the line assuming the word problem follows the linear model. | To extrapolate basically means to assume logically, based on what is given, what any missing information would be. In the case of a line that follows a linear model, you can extrapolate what the line would look like by following the piece of the line given and extending it. | Jack made a CD of his own music and is selling it on amazon.com. In the first week, he sold 4 copies of the CD. After the 6th week, however, he had sold 84 copies. Assuming his sales follow a linear model, (a) Write the linear equation to model his total sales; (b) calculate how many CD's Jack will have sold by the 8th week; and (c) predict how many total CD's Jack will have sold by the 52nd week, if this pattern continues. | First, remember that the amount of CD sales is the y-coordinate and the time in weeks is the x-coordinate. The first week gives you the ordered pair of (1,4) and the 6th week gives you the pair of (6,84). By plugging the pairs into the slope formula, you get (84-4)/(6-1), which ends up being 80/5, and that further simplifies into 16. Next, using the slope-intercept form, y=mx+b, you can plug 16 for the m, and one of the pairs into the y and x values. Using the first week, we have the function of 4=16(1)+b. Subtracting 16 from both sides gives us (-12)=b. Now plugging only the slope and y-intercept (b), we have the linear function of y=16x-12, which is the answer to part a. For part b, all we have to do is plug in 8 (8th week) for the x, to get y=16(8)-12. 16 multiplied by 8 is 128, and 128-12 is 116, which is the amount of CD's sold by the 8th week. For part c, instead of plugging in 8, we plug in 52, since it is the 52nd week. Now, the equation is y=16(52)-12. 16 multiplied by 52 is 832, and 832-12 is 820, which is the answer to the final part of the problem. | Fixed costs means the costs that will always be there each month and will remain about the same every time. Variable costs, on the other hand, depend on how many items are produced and represent the amount needed to produce each item. As variable costs depend on the amount of items produced, there will always be a variable next to them that represents the amount of items sold. The only similarity between the two types of costs is that they take away from the revenue to leave the producer with their overall profit. | Revenue is only what is gained directly from sales prior to deducting the costs. Again, revenue depends on how many items are sold, so there will always be a variable representing the amount of items sold. Profit is the amount gained or lost after deducting the total costs from the revenue. If the costs are greater than the revenue, then the seller/producer loses money. If the costs are less than the revenue, then profit is gained and the seller/producer gains money. If the costs and revenue equal each other exactly, then the break-even point is reached, and no money is gained or lost. | Jack started selling CD's of his own music. It costs $3000 for monthly equipment and rental fees, and 5$ to produce each CD. He sells each CD for 12$. Write his (a) Cost Function; (b) Revenue Function; (c) Profit Fucntion; and (d) estimate the number of picture frames he will have to sell in order to break even (round up to the nearest CD if necessary and find the amount of profit if you do round up). | The fixed cost is $3000 and the variable cost is $5. So, the Cost Function should be C(x)=3000+5x. The revenue from each CD is $12, so the Revenue Function is R(x)=12x. Since the Profit Function is the revenue minus the total costs, the Profit Function must be P(x)=12x-(3000+5x). The next part is the part that needs more thinking and work than the others. In order to break even, the profit must equal zero exactly. So, first we set the Profit Function to zero, making it 0=12x-(3000+5x). Simplified, this is 0=7x-3000. Add 3000 to both sides and then divide both sides by 7 and the answer is 428.57. This makes the break-even point since we must round up. To find out the profit of this rounded BEP, all we have to do is plug 429 into the Profit Function, which makes P(429)=7(429)-3000. This simplifies into 3003-3000 which is 3, so the profit is then 3 dollars at the BEP of 429 CD's | Cost Function is C(x)=Fixed Costs+(Variable Costs)(x), Revenue Function is R(x)=(Price charged for item)(x), Profit Function is P(x)=R(x)-C(x), and BEP is when P(x)=0. | Writing linear models and evaluating for word problems. | None. It takes a little longer to work out problems from concept 7, but none of it is really confusing or too difficult. | borroel_john@yahoo.com | ||||

17 | 6/26/2013 22:21:05 | Bustos | Lorena | In solving a linear problem, two set of ordered pairs must be found first; the x-value represents time and the y-value represents an amount. Then the slope formula (y2-y1/x2-x1) must be used to find the slope. Once that is done, the slope as well as the coordinate with the smallest numbers must be plugged in to y=mx+b. When both the slope and “b” are known, the formula is written in slope intercept form. From there, whatever week of information is desired is plugged in as f(x), meaning the number of the week or amount would be plugged in to mx+b. | The word extrapolating means to estimate a value that falls outside a range of known values. That being said, an example is when connecting two points such as (0,1) and (2,3), we connect those and find only some information, but by extrapolating it, we can find information of greater amounts and importance. | Ruby sells sapphire crystals every weekend at a little shop in Balboa Beach. During week 1, she sells 10 crystals overall. During week 5, because she began painting her hair pink to capture attention, she sold 30 crystals. Assuming her sales follow a linear model, (a) Write a linear equation to model her sales; (b) calculate how many crystals Ruby sold during week 10; and (c) predict how many crystals she will sell during week 15 if this pattern continues. | First, find the coordinates of the linear model, where x represents time and y represents amount; the coordinates turn out to be (1,10) and (5,30). Next, find the slope using y=y2-y1/x2-x1, where the coordinates are plugged in and the answer m=5 is derived (after plugging in as y=30-10/5-1). Then, the slope is plugged in to y=mx+b (and a coordinate as well) and the answer is y=5x+5. For part b, the number 10 is plugged in to 5x+5, revealing an answer of 55. For part c, 15 is plugged in, giving 80 as a final answer. | We have fixed costs, which stay about the same- or exactly the same- each month, or during a certain time period, and variable costs, which represent how much it costs to make each item and vary based on how many items are purchased. They are the same because they are paid during the same time periods but differ because variable costs change and fixed costs do not. | Revenue and profit are different because revenue is similar to how much money will be made per month after selling the items but profit is that minus the costs to keep the business running. If a t-shirt company sells 50 t-shirts by the end of the month and earns $500 in the process, that is the revenue. The profit would be what is left after costs are paid; for example, if in this case the cost to keep the business open and running is $200, then the profit would be revenue minus cost ($300). | Ruby is starting a crystal sapphire company at the beach. It costs $1500 for monthly equipment and rental fees, and $50 for supplies for each crystal. Each crystal sells for $85. Write the (a) Cost Function; (b) Revenue Function; (c) Profit Function; (d) estimate the number of crystals you will have to sell in order to break even (round up to the nearest crystal if necessary to find the amount of profit if rounding up). | Variable costs usually have the x (variable) after them in the formula C(x)= fixed cots+variable costs(x), so the first answer is C(x)= 1500+50x. The Revenue Function is R(x)=__(x), or how much is charged per item (in this case, revenue is R(x)=85x). Profit is P(x)=R(x)-C(x) which would be 85x- (1500+50x). This equation turns into 85x-1500-50x, which ends us with P(x)=35x-1500. BEP is P(x)=0, so in this case it is 35x-1500=0, which leads to 35x=1500, and to a final BEP of around 43 crystals; the profit is found by plugging in BEP to the profit formula from part c- in this case, P(43)=35x-1500, which gives a profit of $5. | In evaluating word problems, the x-value represents time while the y-value represents an amount. In concept 7, Cost (fixed and variable), revenue, Profit, Break-Even-Point (BEP, and PriCe are important terms. | The part I understood the most was the linear models and how to set them up. | I am not confused with any part. | Lore_bustos@rocketmail.com | ||||

18 | 6/27/2013 0:47:15 | Bustos | Jennifer | First we are going to set up two sets of ordered pairs with the x-values representing time and the y-values representing an amount. In the problem we will encounter two statements indicating the time it started to the time it is being compared to. For example week 1 to week 8. We will then put 1 as the x value for the first ordered pair and then 8 as the x value in the second ordered pair. The y values will come from the amount being compared between the period of time that is represented within the x-values. We have to make sure it says its following a linear model. Then we solve for what functions we will need to find. | If we were given two points (2,34) and (4,36) you plot those points on a graph and you connect them giving us only information on what is going on between those two points. That's when you extrapolate beyond those two points and extend the line on the graph to see what is going on on the other end. | Danielle wants to open up a new cupcake shop. She is very excited to finally get to bake all her delicious cupcakes and share them with the world. During her first week of opening her shop, she sells 24 cupcakes. By the eighth week she had sold 248 cupcakes. Assuming her sales follow a linear model, (a) write the linear equation to model her sales; (b) calculate how many cupcakes Danielle sold during week 4; and (c) predict how many cupcakes she will sell during week 26 if this pattern continues. | First we are going to set up two sets of ordered pairs, the x-value representing time and the y-value representing amount. When you read the problem you notice they mention Danielle's first week which represent 1 in the first ordered pair as the x because it is referring to time. The next statement says by her eighth week which will be your x-value for the second ordered pair. The y-values will come from the amount she sold during those weeks for this case week 1 was 24 (your first y-value) and week 8 which was 248 and this will be your second y value. Your two points should end up being (1,24) and (8,248). Now we will be doing the (A) part of the problem. They are asking for the linear equation, which means we will end up with something modeling y=mx+b. The first thing we have to do is plug in our ordered pairs into the y2-y1/x2-x1 to find the slope or m. Once you find m which should equal to 32, you pick one ordered pair and you plug it in to the y=mx+b formula along with your slope. You should have gotten y=32x-8 as your slope-intercept. Now on to step B. It is asking to solve for week 4, you then have to use your f(x) equations and use your slope intercept equation to plug in 4 wherever you see an x. You should end up with f(4)= 32(4)-8. Your answer should be 120 cupcakes. Moving on to part C, they are asking for the 26th week. You repeat the previous step but this time you plug in 26 instead of 4 getting f(26)=32(26)-8 which will equal 824 cupcakes. | There are two different types of costs, fixed costs and variable costs. To get your total cost you need to add up the fixed cost+ variable cost, that will always have a variable attached to it. Fixed costs are like your necessities like the utility bills and the things you need to pay in order to have your business functioning. They're are almost always the same every month. Variable costs can change each month depending on how many items you make. Variable costs depend on how much it costs to make each item and it depends on how many you are making. | Revenue is the money you earn from selling your items. It is the money you receive from the price you are selling your items for. It is how much you are getting from each item you sell. Your profit is what you earn after subtracting Revenue-costs. Its basically what is left over once you have received the money and payed for all your costs. For example if you walk into a store and you purchase a toothbrush priced at $3.00, when you purchase it and you hand the cashier the $3.00 that is the store's revenue. Once the store has sold their toothbrushes for the month, they will then take their revenue and subtract their costs from it to be left with an earned profit. | Danielle saw that her cupcake business was such a hit, that she decided to open up a second cupcake shop. It will cost her $2,500 for monthly equipment and rental fees, and $2.50 in supplies for each cupcake. Danielle sells each cupcake for $4.00. Write your (a) Cost function; (b) Revenue function; (c) Profit function; and (d) estimate the number of cupcakes Danielle will have to sell in order to break even. | The first thing we need to is find our cost function. The general formula for that is C(x)= fixed costs+ variable costs (x). We need to plug in $2,500 as our fixed cost because that is what we need to pay monthly to run the business. Second we need to plug in $2.50 as the variable cost because that is how much each cupcake will cost to be made so we will add an x at the end so its looks like $2.50x. Your cost function should be C(x)= 2,500+2.50x. Now part B, your revenue function should be the $4.00 because that is how much Danielle is selling each cupcake for. The formula for revenue is R(x)= which in this case is 4x. Part C is asking for the profit function which is P(x)=R(x)-C(x). You simply plug in your cost function and your revenue function into the profit equation. You must distribute the minus sign to the cost equation once you have plugged it in. It should look something like this after you have plugged it in and distributed the negative: P(x)=1.50x-2500. Once you have reached this step, you solve it through by solving for x. You move -2500 to the other side giving you 2500=1.50x. Then you divide by 1.50 to both sides to isolate the x on one side and you should end up with x=1,666.66. Since you cant have .66 of a cupcake, you must ALWAYS round up if you don't end up with a whole number because you cant sell someone .66 of a cupcake. After you round up you should end up with x=1,667. This will be the number of item you need to sell to reach your break even point. Now for the final part D we will estimate the number of cupcakes Danielle will have to sell in order to have a successful business. You then use the equation P(x)=0 to find your profit. You plug in x=1,667 into the simplified Profit equation P(1667)=1.50(1667)-2500. The very small profit should equal $.50. | Cost-variable and fixed, Revenue, Profit, BEP, extrapolate, linear model, x value-time, y-value amount | it was all understandable. | extrapolate | jennybustos97@live.com | ||||

19 | 6/19/2013 18:00:13 | Caballero | Rita | To solve a linear model you have to first take the numbers and put them in two sets of coordinate points. After that take the points and plug it in in equation to find slope. after you have found your slope you choose whatever coordinate point you want and your slope and plug it in in slope intercept form to find b. after you have b then plug that in to have your equation of the linear model and instead of having y= replace it with f(x). After you have that you can solve for the rest using that equation. | Extrapolating means to extend something., An example is extending or extrapolating a line on a graph. | Joshua likes this girl named Raelynn. Raelynn likes roses and Joshua wants to giver her roses. On the first week Joshua collect 5 roses. On the sixth week he collects 35 roses. Assuming that his collection follows a linear model, a) write the linear equation to model his hunt for roses; b) calculate how many roses he collected on the third week; c) and predict how many roses he will have by the 15 week if this pattern continues. | The first thing you have to do is put the numbers in order pairs they should be (1,5) (6,35). After that use the points and find slope. after you have solved for slope which should be 6, you use the slope and any pair of points and put them in slope intercept form. when you have done that your equation should be f(x)=6x-1. after you have your equation solve for b and c using this equation. for part b plug in 3 and you should get 17 roses and for c plug in 15 and you should get 89 roses. | The two different types of costs are fixed costs and variable costs. One way they are similar is that these costs are not making us money they are making use pay something. Fixed costs is something that we have to pay monthly like a phone bill and a variable cost is how much it costs to make something. | The revenue is how much we will charge for an item we sell. The profit is taking your revenue and subtracting the costs to see how much you guys make. An example of revenue is charging 3 dollars for a lipstick you make and your profit is subtracting your revenue and your costs to see what you make for example 1.50 can be your profit for each lipstick you sell. | Joshua and Raelynn are starting their own rose business. It costs them $1750 for monthly equipment and rental fees, and $2.50 for the rose supplies. They sell a single rose for $5. Write the a) cost function, b) revenue function c) profit function, d) estimate the number of roses they will have to sell in order to break even. | a) the cost function is c(x)=1750+2.50x (fixed costs + the variable expense) b) the revenue function is r(x)= 5x ( how much you charge for the rose) c) the profit function is p(x)=5x-(1750+2.50x). from here you have to distribute the negative to the parenthesis and then combine like terms and your profit function should be p(x)=2.50x-1750. d) to estimate the number of roses they will have to sell to even out all you have to do is set the profit function to 0 and add 1750 to zero and then divide 1750 by 2.50 and the answer should be 700 roses. | I have to remember is to always put parenthesis when solving for f(X) also I have to remember what numbers go where in the equations. | I understood everything from these two concepts | I am not confused on anything in this concept I just have to watch out for little mistakes on my adding and subtracting. | ritacaballero54@yahoo.coom | ||||

20 | 6/28/2013 7:31:31 | Camero | Jasmine | You have to find the amount of time it started and then the second time the problem gives you. Then, you find the equation to model the numbers given. Next, you plug in the numbers you are looking for to solve. | It means to find what is in between. For example, if you were given to points you could extrapolate what was in between those two numbers by using the given information. | Jasmine likes to make her own bows for hair to sell to her friends, Within the first week she sold 6 bows. During the 5th week she sold 24. Assuming it follows a linear model, (a) write the linear equation, (b) calculate how many bows Jasmine sold during the 3rd week, (c) predict how many bows Jasmine will sell during week 23. | First make two sets of ordered pairs of the time given and the number sold during that time given (1,6) (5,24). Then you find the slope of the ordered pairs and after that you find the value of "b" in slope-int form (y=9/2-3/2). Following that you plug in the numbers you are trying to solve for in the equation. 3rd week = 5. 23rd week = 96 | Fixed costs are the same and maintain a certain cost for usually about every month. An example of fixed costs would be paying the rent, it never changes going from month to month. Variable costs vary. Unlike fixed costs, the amount doesn't stay the same. | Revenue describes the amount you charge for an item. Profit is the amount of money you make from the charge of the item after paying for all of the expenses. For example, if you buy candy for 25 cents and sell it for a dollar then that is your revenue. Profit would be the amount of money you would make after you take your revenues and subtract all of your costs. | Jasmine started bookmark selling business. It costs $1300 for monthly equipment and rental fees, and $o.45 for the supplies for each bookmark. Jasmine sold each bookmark for $0.95. write (a) cost function (b) revenue (c) profit function (d) estimation of the number of bookmarks needed to be sold to break even. | First you write the costs equation (1300+0.45x). Then the revenue equation, which is what you sold it for (0.95x). Next, you solve for profit which is the revenue minus the costs (0.5x-1300). Then you solve for BEP by adding 1300 to both sides. The answer is 2600 bookmarks. | Learning how to write and solve linear models and the different types of costs, revenue, profit, and break-even point. | Solving linear problems and understanding the business vocabulary. | Everything is understood. | jasminec97@gmail.com | ||||

21 | 6/27/2013 13:08:41 | cardenas | vanessa | The first step to solving a linear model is to set order pairs from each problem. Then you have to plug in the points into y2-y1 / x2-x1, in order to find its slope. Then you have to find B and get a linear equation. The word problem should ask to find or solve for a different set of ordered pairs giving you the X. Plug in the x back into the equation and then you get your answer and a complete ordered pair. | extrapolating means to estimate. for example in math it is used to estimate values within a known range by assuming that the estimated value follows logically from the known values. | Sarah is starting a fashion store. She has many interesting ideas for her upcoming line. In her first week of opening the store she sold 6 dresses. By the 6th week she had sold 121 dresses. Assume her sales follow a linear model, a)write a linear equation to model her sales.b) calculate how many dresses she will sell on her 9th week, c) and predict how many dresses she will sell in her 21 week if the pattern continues. | First of all, write the ordered pairs that were given in the equation. Then use the formula y2-y1/x2-x1. You should of gotten 23 as your slope. then plug it into the equation y=m(x)+b, plug in one of the ordered pairs and solve for b. The b in the equation should be -17. the linear equation should be y=23x-17. If we want to calculate how many dresses she has sold in week 9 you plug in f(9) into the x. You should have gotten 190 dresses for week 9. For week 21 we plug in f(21) into the equation and substitute it for x. So 23(21)-17 is 446 dresses. | The two costs we have are fixed costs and variable costs. Fixed costs are for monthly costs such as bills ect. Variable costs is the cost that it takes to make the product or items being produced. Variable costs also vary on how many items you make. | Revenue is how much you charge for something. For example a sock company who sells socks for 10 dollars revenue is 10 dollars. Profit is what you are left after you pay for all the costs of the items . If the sock company pays 2 dollars to make the pair of socks and sells them for 10 dollars their profit is 8 dollars. ( not including the other monthly costs) | It costs Sarah 1300 for monthly equipment and rental fees and 5.25 for supplies for each dress. She sells each dress for 25 dollars. write you a) cost function; b) Revenue function; c) profit function; d) estimate number of dresses she has to sell in order to break even ( round up to the nearest dress if necessary and find the amount of profit if you do round up. ) | First of all write the costly equation. You should get C(x)= 1300+5.25(x) Then write the equation for the revenue. You should get R(x)= 25(x) . Then the profit equation which should be P(x)=25(x)- ( 1300-5.25x). it changes into 25(x) - (1300 +5.25x). Combine like terms so P(x)= 19.75x - 1300. Next you equal the profit equation to equal to zero in order to break even and solve. P(x)= 19.75x- 1300=0 p(x) should equal to 65.82 meaning she has to sell 66 towels to break even. with 3.50 dollars left over as profit. | the vocabulary words. | how to solve for both concepts. | remembering all of the steps in order. | vanessa_xo18@yahoo.com | ||||

22 | 7/12/2013 23:47:20 | Cardenas | Cecilia | The first step is to translate the word problem into coordinates, in which x=time and y=amount. Then you need to find the slope of the coordinates and then plug in a set of the coordinates and find b. Lastly you plug in the week number of whichever the problem asks you to solve. | The word extrapolating means to use the linear model to estimate the result of a future week or time period by following the pattern. It means to find the result of a future time after about 5 weeks. | Mindy loves to bake cupcakes and one day decides to sell them. During her first week of sales, she sells 5 cupcakes. By week 4 her baking skills grow popular and she sells 20 cupcakes. Assuming her sales follow a linear model, (a) write the linear equation to model her sales; (b) calculate how many cupcakes she sold by week 3; and (c) predict how many cupcakes Mindy will sell by week 10 if this pattern continues. | First you have to translate the time and amount into coordinates which would be (1,5) and (4,20). Then you would find your slope (m) by using the slope formula, so it would be 20-5 over 4-1, which equals 15/3 which is equal to 5, which is your slope (m). Then you plug in your m(5) into the equation mx+b=y and use one of the coordinates, whichever you prefer is fine. So it would be 5(1)+b=5, which equals 0. So your equation (a) would be 5x=y. To solve (b) you need to plug in 3, because that is the week we need to calculate so it would be 5(3)=15, so she sold 15 cupcakes during week 3. And finally to solve (c) you would do the same as you did in (b) so it would be 5(10)= 50, so she would sell 50 cupcakes by week 10 if the pattern continues. | We have fixed costs and variable costs. Fixed costs is a monthly cost which usually doesn't change because it is usually a set price for every month. However, variable costs usually do change because it is a cost depending on how much it costs to make an item and usually changes depending on how many items are sold each item. | Revenue is how much you charge other people for the merchandise you sell. Profit is how much you made from the total sales after subtracting all the costs you had to spend money on. For example you buy a box of 30 bags of chips for $12 and you sell each bag for a $1, the revenue would be $1 and your profit would be 30($1)-$11= $19. So the $19 is your profit after subtracting the cost of the box of chips. | Mindy is starting a bracelet selling business. It costs her $1000 for monthy equipment and rental fees and $2.00 for supplies for each bracelet. She sells each bracelet for $5.75. Write your (a) cost function; (b) revenue function; (c) profit function; and (d) estimate the number of bracelets she has to sell to break even. | First you find your (a) which is C(x)= $1,000+$2x because those are your fixed and variable costs. Then you find your (b) which is R(x)= $5.75x. After you find your (c) P(x)= $5.75x- $1,000+$2x which breaks down to $5.75x-$2x= $3.75x- $1,000. You add $1,000 to each side to get the equation of 3.75x= 1,000. To solve (d) you use that equation and get 266.66 as the BEP of 266.66 and you have to round up to 267. Then you plug in 267 to find the profit so it would be 3.75(267)= $1001.25-1000= a profit of $1.25. | The most important things I need to remember is the concept of linear models and how to solve them, extrapolating and its definition, the terms for business problems such as cost, revenue, profit, and BEP. | I understood concept 6 the most because there is only 1 equation that i need to remmeber unlike concept 7 which has an equation for profit, revenue, BEP, and all the costs. | I am not confused on any of these so far, i understand it pretty clearly. | ceci071997@yahoo.com | ||||

23 | 8/14/2013 2:16:31 | Carranza | Gabriel | First you find the order pairs. Then you find the slope. Next you plug in the numbers that are given. | to estimate something | Arturo loves to draw. He is drawing pictures for his dad. He is planning to give him the drawings in 4 months. During the second week he drew 4 drawings. By the 8th week he made 36 drawings. Assuming completion of problems follows a linear model. (a) write the linear equation to model the number of extra problems he has done; (b) calculate how many drawings Arturo has done in week 5. (c) Predict how many drawings Arturo will have in week 15, assuming the patterns continues. | When you finish reading this you need to try to find the ordered pairs. The ordered pairs is (2,4) (8,40). Next you will try to find the slope. You will use the midpoint formula. The answer you should get is f(x)=6x-8. Then the question asks how many drawings does Arturo have done in 5 weeks. You plug in the 5 in f(x). So you should get something like this f(5)= 6(5)-8. The answer you should get is 22 drawings. Then the other question says predict how many drawings Arturo will have in week 15. You plug in the numbers like so f(15)= 6(15)-8. The answers you should get is 82 drawings. | The two different cost we have are fixed cost and variable cost. Fixed cost | Revenue is how much you are charging the person. Profit is how much you have left over. If my company were to pay for a baseball bat from a factory for 150 and I decide to sell it for 300 dollars(thats my revenue). I would have 150 dollars left over. That would be my profit. | Arturo is starting a baseball company that specifically makes baseballs. It cost him 1600 dollars for the monthly equipment and rental fees, and $.50 for each baseball. Arturo sells each baseball for $3. Write your (a) Cost Function; (b) Revenue Function (c) Profit Function; (d) estimate the number of baseballs Arturo has to sell in order to brake the even number. | First you write out the cost. C(x)= 1600+.50x. Then you write out the Revenue like so R(x)=3x. Next you write out the profit P(x)=3x-(1600-.50) Distribute the problem and combine like terms. The breaking even point is 640 baseballs. | Underline as you read the word problems. | Linear models and evaluating | nothing | gabscarranza@yahoo.com | ||||

24 | 6/27/2013 19:46:59 | Castillo | Joe | First identified the time (x-value) and the amount (y-value). Then do the point slope form to get m. Next do the slope intercept form to get b. Finally plug in whatever time in the x to get the amount. | To go further from the known ranges. | Pancho collects games from GameStop. During week 1, he collected 5 games. In week 8, he collected a total of 40 games. Write the linear equation to model his collection, predict how many games Pancho collected in week 4 and predict how many games he will collect in week 12 if this pattern continue. | First plug in the values in the point slope form to get m, m=5. Then do the slope intercept form and plug in the values to get b, b=0. Finally plug in for week 4 and 12 to get the amount of games Pancho collected. Week 4=20 games and week 12=60 games. | Fixed cost is what you have to pay every month like cable or Internet. Variable cost is how much money you wast each month to make each item, so it depends on how items you make each month. | Revenue is how much you charge for each item and profit is how much you gain from selling the item. | You are starting a eraser business. It costs you $2500 for monthly equipment and rental fees and $.50 for supplies for each eraser. You sell each eraser for $1.50. Write your cost function, revenue function, profit function and estimate the number of erasers you will have to sell in order to break even (round up to the nearest eraser if necessary and tell how much profit you will make if you have to round up). | Get the cost function c(x)=2500+.50x and the revenue function R(x)=1.50x. Then get get the profit function P(x)=1.50x-(2500+.50x) then simplify x=2500. Finally get the amount of many from the profit, you gain nothing | Know that the x-values represent time and y-values represent the amount in linear models. Know the cost, revenue, and profit function. | I understand concept 7 the most. | No confusion. | Joecastillo12@live.com | ||||

25 | 6/28/2013 13:18:25 | Castillo | Beatrice | First read the problem then take notice that you can set up two sets of ordered pairs and then you use m=y2-y1/x2-x1 to solve for the slope. Then plug in one of the ordered pairs and slope into the slope intercept form which is y=mx+b to solve for b. After doing so plug in the slope(m) and b into the equation y=mx+b and that will get you the linear equation to model whatever the problem asks. | Extrapolate means to estimate a value that falls outside of range of known value | Betty likes to draw on the weekends. During week 1, she drew 4 drawings. During week 5, she enough time to draw 24 drawings. Assuming her findings follow a linear model, (a) Write the linear equation to model her drawings;(b) calculate how many drawings will Betty have during week 3; and (c) predict how many drawings she will have during week 20 if this pattern continues. | first read the problem and then you will notice that the first week and fifth week can translate to the x-values and the number of drawings can translate to the y-values and with this you could make the coordinates (1,4) and (5,24). Then you will write a linear equation by first using m=y2-y1/x2-x1 to find the slope which will go like this when plugged in m=24-4/5-1=20/4=5 then you will use y=mx+b. Plug in # into equation like this 4=5(1)+b then subtract 5 which will then give you b=-1. Plug results into y=mx+b which will look like this y= 5x-1. To calculate how many drawings Betty had during week 3 simply plug in # to equation like this f(3)=5(3)-1 which will result in her having 14 drawings. Same for week 20 plug it into equation like this f(20)=5(20)-1 which will result in Betty having 99 drawings. | The two different types of costs we have are fixed costs and variable costs. Fixed are things that are paid monthly like the utilities and they usually stay the same every month. Variable cost vary on how many items are made and how much it cost to make each item. Variable costs are followed by variables (x). They both are in the same equation. | The difference between revenue and profit is that revenue is how much you charge for each item sold and profit is how much is left after everything is paid for like the bills. For example someone can sell markers for $3 and will be determined with equation R(x)=3x. A profit will be the revenue minus the cost and what is left or P(x)=R(x)-C(x). | Betty is starting a drawing business. it costs $1500 for monthly equipment and rental fees, and $5 for each drawing. She sells each drawing for $10. write your (a) cost function;(b) revenue function;(c) profit function; and (d) estimate the number of drawings she will have to sell in order to break even. | first you read the question and then you find the cost which will be fixed -1500 and variable 5 and will be put into equation that looks like this: C(x)=1500+5x. Then solve for revenue function which is R(x)=10x because its $5 per drawing and the profit will be P(x)=(10x)-(1500+5x) which will equal to P(x)=5x-1500. Then equal equation to zero like this P(x)= 5x-1500=0 then add 1500 and divide like this 5/1500= x=300 drawings and since there is no decimal to round there is no break even point. | The important things I need to remember are the step by step process of how to solve linear model word problem, what cost, revenue, profit, and break-even-point mean, there equations and how to solve cost, profit, and revenue problems step by step. | I understood everything from these two concepts. | I am not confused about anything on the two concepts. | castillo.beatrice@yahoo.com | ||||

26 | 6/29/2013 18:32:59 | Cecere | Michael | First you got to get the ordered pair from the word problem. Then you got to use those to find the slope using the slope formula. Plug in the slope and one of the points from the order pair to get b. After you have done this you will have the linear equation. Using the linear equation you can plug in whatever the problem then asks of you to do. | Extrapolating is when you use two points and a linear equation to find unknown points elsewhere on the line. For example, if I know the points (1,11) and (6,111) and the linear equation is f(x) = 6x - 2, then I could extrapolate other points on that line without having to plot a graph with every point in between. | Sir Liftsalot is trying to beef up for the ladies. During the first week of lifting, he gains 5 pounds. By week 6, thanks to a lot of supplements and swag, he gains 115 pounds. Assuming his bulking up follows a linear model, (a) write the linear equation to model the pounds he gains, (b) calculate how much he gained in week 3, and (c) predict how much Sir Liftsalot will have gained by week 18, assuming the pattern continues. | First you get the points (1,5) and (6,115) and you calculate the slope to be 110/5 which is equal to 22. Then you plug the slope and (1,5) into y = mx + b and you get the linear equation which is f(x) = 22x - 17. For (b), you will use f(3) and you shall get 49 pounds. For (c) plug in f(18) and you get 379 pounds. | The two types of costs are fixed costs and variable costs. Fixed costs are paid monthly and they are like bills such as for utilities and rent. Variable costs are how much it costs to make each item and the costs vary monthly based upon how much items you want to produce. | Revenue is how much you charge for a certain product. Profit is how much money you actually receive after you have taken your revenue and subtracted it from your costs. For example, if I owned a shoe business my revenue would be how much the shoes are sold for and my profit would be the amount of money I receive after I pay for costs. | Sir Liftsalot is running a supplement store. It costs $2500 for monthly equipment and rental fees, and $1.25 for supplies. He sells each protein packed supplement for $25. Write his (a) cost function, (b) revenue function, (c) profit function, and (d) estimate the number of supplements he will have to sell to break even (round up to the nearest supplement if necessary and find the amount of profit if you do round up.) | For part (a), you take the costs and add them together to make the cost function. This should come out to C(x) = 2500 + 1.25x. For (b), you will plug in the revenue (25) into the equation for revenue function. This will be R(x) = 25x. Next you will take those two equations and subtract the costs from the revenue to make profit. It should be P(x) = 23.75x - 2500. Then, you take that equation and set it equal to zero to find your break-even point. When you solve that it should be 105.26 which you round up to 106 supplements. Now you got to figure out the profit since you rounded. Just plug it in to the profit function and you will see it is $17.50 profit. | the vocabulary terms of costs, revenue, profit, and break-even point, and how to use linear models. | Evaluating linear models. | nothing, fully understood. | cecere444@yahoo.com | ||||

27 | 6/27/2013 23:25:01 | Ceja | Vanessa | First, you have to set up the two points according to the problem. For example, "on the first week Patty collected 4 bills and on the third week she had 66", so the two points would be (1,4) and (3,66). Then, for step A, you would have to get the equation into slope intercept form and so in order to do so, you would find slope with the slope formula and then plug in any of the two points you have to find the y-intercept. In the end you can just equal your equation to zero. For step B, you just plug in the number the problem gives you and use it as if it were f(x). Same for step C depending on what they ask for or the amount of days, weeks, units then just plug in and solve. | The word "extrapolating" means that you would extend the line beyond the two points given since you do assume that it follows a linear model. For example, if your two points were (1,2) and (4,5) then after plotting them, although you would only have a part of the line, you would extrapolate, extend it, and go beyond the points. | Sofia loves competing against her older brother and they always make bets with each other just for fun and they simply get along very well. So, one day, Sofia made a bet with him and said that she could earn more money than him within a month by working for it. Her brother accepted the bet. During the first week she earned 20 dollars and during the third week she earned a total of 300 dollars. Assuming her earning of money follows a linear model a) write the linear equation to the amount of money she had earned; b) calculate how much she earned by the second week; c) predict how much total money she will have earned by the fourth week. | First I would take my two points and write them down, in this case they would be (1,20) and (3,300). Then, to solve for A and get my equation, I would find the slope and the y-intercept by using the slope formula and then plugging in one of my points to get the intercept. Then, moving on to B I would use f(x) and plug in 2 to my linear equation, since that is what it's asking for (the second week). I would solve it and get an answer, then lastly I would plug in 4 in f(x) again for step C. I would get another answer and end up with all three parts: A, B, C. | The two different types of costs that we have are fixed costs and variable costs. Fixed costs are what is payed monthly that stays just about the same amount like rent and the utilities needed. While that is that, variable costs is the amount you need to make each item which may change depending on the amount you wish to produce and make. | Revenue is the amount of money that you charge for each item that you are selling. For example, if you are sell chocolates the revenue is the cost of the chocolates. Now, profit is something to be happy about since it's the money that you earn. You would take the revenues and subtract your costs. For example, if my revenues was 60 dollars and the cost was 40, I would subtract that and my profit would be 20 dollars. | You are starting a Chocolate Factory business. Your business is full of sweets and chocolate of course like strawberries covered in chocolate, etc. It costs you $2000 for monthly equipment and rental fees, and $0.25 for supplies for each chocolate. You sell each chocolate for $0.75. Write your (a) cost function; (b) revenue function; (c) profit function and (d) estimate the number of chocolates you would have to sell in order to break even. | First to find (a) I would take the cost and add it to the cost for supplies, so in this case it would be 2000 + .25x. The (x) is for the quantity. Then for (b) I would simply put the revenue multiplied by x which is the amount once again. For example it would be .75x. Then, for (c) it gets more troubled because I would take the revenue and then subtract the supply cost to the total cost. So it would look like this= .75x-(2000+.25x). I would have to be careful and make sure to remember the parenthesis. Lastly, to find the total cost, (d), I would solve the equation from (c) by distributing the negative outside the parenthesis and then equaling it to 0 to solve. Rounding would be necessary. | The most important facts and terms I need to remember is how to get the two points from reading the problem and being able to solve an equation like f(x) and basically know slope and the formula. Another thing, for cost, profit, and revenue i have to understand what numbers from the problems go to each, goes to the cost, revenue, and profit. | I understood both concepts pretty evenly. One part that seemed very simple was having to get your two points when writing linear models. | I am not confused on these concepts so far. | vanessaceja95@yahoo.com | ||||

28 | 8/12/2013 11:44:14 | Chamu | Jesus | We first have to find the two order pairs that they give us in which x mean time and y mean amount after that we solve for the slope by by using m=y2-y1/x2-x1. after the slope we solve b in which we solve by using y=mx+b. | it basically mean giving a bit of information and with that info be able to predict the outcome of future sells. | Juan is starting to collect baseball cards. in his first week he collected 6 cards in his 6th week he collected 41 cards. A.) write a liner model of his collection. | first we start by solving for the slope which would be 41-6/ 6-1= 7 then use one pair and he slope and plug it in to y=mx+b 6=7(1)+B SO B WOULD EQUAL -1 and after that we already have our answer which would be Y=7x-1 | Fixed cost is bills paid every month like water gas and rent. variable cost is the money spent on supplies you use to create an object. | revenue is the cost of the object your trying to sell. profit is the amount of money you truly make after you pay off all you're bills. | juan is trying to sell shoes. it cost him 2000$ for monthly equipment and rental fees he spents 2$ for the supplies to build eac shoe pair. He sells each shoe for 20$ each pair. A.) Cost function B.) revenue function C.) profit function D.) BEP | A.) not hard to solve C(x)= 2000+2(x) B.) R(x)=20(x) this is the amount money you make from each sell C.) P(x)=18x-2000 D.) now we find the estimate 0=18x-2000 so we add 2000 to both side then we divide each side by 18 and we get 111.11 but we much push it to 112. juan must sell 112 pair of shoes to break even point. | the profit and BEP fromula | liner models | Business problems. | jesuschamu@yahoo.com | ||||

29 | 8/2/2013 22:05:31 | Chavarria | Kathy | Step 1: read out the key factors for the X and Y points that are hidden out in the story Step 2: find the slope of the two given points that you have found Step 3: You create the equation using the slope and one of the points, you can either use slope-intercept formula or point-slope form to find your B value Step 4: If given to find a pattern for let's say the number three plug it into your equation and solve until you reach the answer | Extrapolating means when you predict what will come afterwards due to the consistency that goes on throughout a certain amount of time. Ex: When you are at home and you notice that your roommate always goes out every four days and comes back with bread, you will estimate that in 20 days later she will go out and get some more bread | There once was a dog named Hershey and he loved to wait for his masters at the front of the door with his favorite chew toy. The first week he did this, his maters played with him for three hours. But when it was his tenth week, his masters played with him for 34 hours in total. Assuming that their playing hours follow a linear model, A) write the linear equation to model their play time; B) calculate how many times they played for 5 weeks; and C) predict how many more hours they would play for their 23 week. | Okay so you first highlight the weeks (X) and hours (Y) that we are given, then you are to use those two pieces of information and find the slope using the Y2-Y1/X2-X1, when you get the slope you then plug it in to the point-intercept formula with one of the points that were given to you. After you find the the B value you can then finally create the equation that we are to find. Then you simply plug in the 5 into the X and solve for you can get the answer for the second part and you do the same for the last question as well. | Fixed Costs: Differences- how much we pay monthly; stays about the same every time Variable Costs: Differences- how much it costs to make each item; cost varies Fixed & Variable Costs: Similarities- They are both used for business and are important to know if you want to start to know how to earn profit and start a new job | Revenue: it is how you much you charge for the item that you are selling Profit: How much you are earning in total after spending most of the money for the costs | Hershey one day decided that he should open up a Bone Bakery for all of his neighborhood buddies can go and have a bite to eat. It costs him $1200 for monthly equipment and rental fees, and $2.25 for supplies for each bone bread. He sells each Bone Bread for $4.50. Write for his (a) cost function; (b) Revenue-Function; (c) Profit-Function; and (d) estimate the number of bone breads he will have to sell in order to break even (round up to the nearest bone bread if necessary and find the amount of profit if you do round up). | So first you highlight the key factors like the monthly equipment and rental fees, supplies, and how much he sells the bone bread for. Then with the monthly equipment and rental fees and supplies (1200+2.25X) you put it down as the cost function. The Cost of the Bone bread will be the equation for the revenue function (4.5X). For the profit function you just subtract the cost function to the revenue function (4.5X-(1200+2.25X)). You will have to simplify it for it can become the profit function. When finished with that you just have to equal that equation to zero and simplify. If it turns out to be a fraction just round up to the nearest number and look for the profit number by plugging everything back in. | Profit; Cost (fixed and variable); Revenue; Break-Even Point; Extrapolating | Was writing linear models and evaluating for word problems | On writing and solving Cost, Profit and Revenue word problems | chavarriakathy92@hotmail.com | ||||

30 | 6/27/2013 22:30:03 | Chavez | Sarah | From the word problems, there will be two sets of ordered pairs. The x-value represents time and the y- value represents an amount. After finishing reading the word problems, take out the information that is needed (the two set of ordered pairs). The next step is to find the slope using the equation m=y sub 1 –y sub 1/ x sub 2-x sub 1. After figuring out the slope, plug it in to slope-intersect form, y=mx+b, with one of the ordered pairs from the word problem to get the linear equation. Then calculate a time between the two ordered pairs. And last extrapolate. | Extrapolating means to extend, or expand known data by assuming that the data follows logically from the known values. For example, Luna's BBQ restaurant has 10 customers in the first week and 90 during the 6th week. We want to predict how many customers she will have in 43 weeks, assuming the customers pattern follow a linear model. If the linear equation is f(x)=16(x)-6, then we just have to plug in 43 where "x" is. Multiply 16 an 43 to get 688 then subtract 6 to get 682. We predict that she will have 682 customers in 43 weeks. | Luna wants to start her own BBQ restaurant. During the first week, 10 people eat at the restaurant. During week 6, because her restaurant had high reviews 90 people ate at the restaurant. Assuming the people eating at the restaurant follow a linear model, (a) Write the linear equation to model her customers; (b) calculate how many customers Luna had during week 3; and (c) predict how many customers will she have during week 23 if this pattern continues. | The first step is to know the two set of ordered pairs, which is (1,10) and (6,90). The we have to find the slope using slope formula(m= 90-10/ 6-1). We get the slope of 16. Then we plug 16 and a ordered pair into slope-intercept form. (Ex. 10=16(1)+b). Next we have to find b in the formula. Multiply 16 and 1 to get 16, then subtract 16 from both sides to get -6=b. The linear equation is f(x)=16(x)-6 (part a). Next we need to calculate how many customers Luna had in 3. Basically we plug in f(3) to 16(x)-6. Multiply 16 and 3 to get 46 and the subtract 6 to got 40 customers in the 3rd week. For part c, we want to predict how many customers Luna will have in week 23. Same thing like part b, we just plug in 23 to the linear equation. So multiply 16 and 23 to get 368 and then subtract 6 to get 362 customers. | There are two different costs, fixed costs and variable costs. Fixed costs is paid monthly, which stays about the same every month while variable costs is how much it costs to make each item. Cost varies monthly based on how many items you decide to produce. Both equal the cost equations. | Revenue is how much you change for each item you sell, R(x). Profit is when you take your revenues and subtract your costs, P(x)= R(x)-C(x). For example, Luna is starting a charm bracelet business. (These bracelets can be personalized.) It costs her $5000 for monthly equipment and rental fees, and $12 for supplies for each bracelets. She sells them for $22. The revenue is R(x)=22(x). The profit is P(x)= 22(x)-(5000+12x) | Luna is starting a charm bracelet business. (These bracelets can be personalized.) It costs her $5000 for monthly equipment and rental fees, and $12 for supplies for each bracelets. She sells them for $22. Write your (a) Cost Functions; (b) Revenue Function; (c) Profit Function; and (d) estimate the number of bracelets she will sell in order to break even. | First we need to know which numbers go with which function. We need to find the cost function which is C(x)= 5000+12(x). Then we need to find revenue function which is R(x)=20(x). Next we find the profit function which is P(x)= 20(x)-(5000+12x) or when expanding it, 6x-5000. The last part is to find the break even point. We make 6x-5000 equal to 0. Then add 5000 to both sides to get 6x=5000. Next divide 6 to both sides to get 833.33. However we want a whole number so we round up to have 834 bracelets. When we plug it back into 6(834)-5000, it equals $5. | When evaluating linear models, x-value represents time and y-value represents amounts. Make sure with word problems, the answers have units at the end. Remember with business problems to use “Price”. Make sure to round up when dealing with profit. | The part I understand the most is writing linear models and evaluating for word problems. | I understand both concepts and nothing confuses me. | sarahchavez2009@gmail.com | ||||

31 | 7/1/2013 21:01:46 | Chavez | Erick | step one would be to find the two coordinates. x is represented by time and y is represented as the amount. in step two you will need to find the slope. in step three you need to find B. step four you write you equation using y=mx+b. after that you use the equation to find the amount with the given time that they give you. | extrapolating means that if you plot the points on a graph it only gives you information on a certain part but by extrapolating we continue the line and finds out what happens at the other end. an example would be on a graph. if they were to give us a line and we wanted to keep the line going. | Toby likes to sell brownies. he works in an office and his co-workers are his main customers. on his first week he sold 50 brownies. during his 4th week he sold 95 brownies. Assuming his sales follow a linear model, (a) write the linear equation to model his sales; (b) calculate how many brownies he sold during week 2; (c) predict how many brownies he will sell by week 10 if the pattern continues. | first you would find your coordinates which are (1,50),(4,95). then you would find your slope which is 15. next you want to find your B so you plug in your coordinate (1,50) and your slope 15 to y=mx+b. Your B=45. your linear equation is y=15x+45. to find how many were sold on the 2nd week you plug in 2 to x and you get 75. Same to find the 10th week you plug in 10 to x and get 195. | we have fixed cost which is like the light,water,and electric bill. it stays constant and wont change. then we have our variable cost which tell us how much it cost to make the product and we control how many we make. | revenue is how much you get for one item. (how much you sell it for) Profit is how much you get after the subtraction of the revenue and cost. an example would be when the cost is $1000 for rent and $2.00 for supplies and the revenue is $6. your profit would be 6 - (1000 + 2x) | Toby started selling brownies for a business. His gas bill went up by $80 since he started using the stove more. its cost him .75 cents in supplies for each brownie. he pays no rent since he sells them at his office. he sells each brownie for 2.00. write your (a) cost function; (b) Revenue Function; (c) Profit Function; (d) estimate the number of brownies he will have to sell in order to break even. round up the the nearest brownie. | first you have to find the cost function which is the fixed cost and the variable cost. C(x)=80+.75x. then to find the revenue function we see how much he sells it for which is R(x)=2x. the we have to find the profit function we subtract the revenue and the cost and we get P(x)=1.25x-80. and to find the amount of brownies he would have to sell to break even we make the profit function equal to zero and get 64 brownies. | (week #, books sold) | writing linear models an evaluating for word problems. | i understand all concepts | erickchavez.97@me.com | ||||

32 | 8/26/2013 15:13:06 | Chavez | Jose | The first step is to find the ordered pairs which you get when you take the time and use that as x , then you get the amoun and use that as the y. Then you get the ordered pairs and you have to try to find the slope by using the equation and once you find that you take the. Slope and then you try to find the b with slope intercept form and you plug in only one of the ordered pairs for this and then solve. | It means you guess based on what you already know. Like for example, we can now extrapolate the patients condition after reviewing their stats. | Jack collects rocks by the lake. During week 1 he had collected 10 rocks. During week 7 he had collected 70 rocks. Assuming his collection follows a linear equation (a) write a linear equation for his collection.(b) calculate how many rocks he will have collected by week 4(c)predict how many rocks he will have collected on his 20 th week if the pattern continues | 1. Find the two ordered pairs which are (1,10) and (7,70) 2. Take the two orders pairs an try to find the slope by putting (70) - (10) over (7) - (1) and solve. That should give you the slope. 3.plug in one of the ordered pairs and the slope in a slope intercept equation and you solve to find the b. 4.once you have foun the answer you equation should look like this f(x)=10x since the slope was 10 and the b was 0. 5. Then you just take that equation and put the values you need to find for the rest of the problems | Fixed costs and variable cost are very different. Fixed costs stay the same every time you payed and never change. Variable costs are costs that don't stay the same when you pay and depend on when you want and how much it's costs to produce that product. You need them both in order to solve the problem and they are both for the equation c(x) and they are costs I order to make the product you are producing . | Revenue is what you charged for an item and profit is what what you get when you subtract the revenue with the cost it takes to make it. For example if I sell a shirt for 5 dollars it is your revenue and the profit is what you get when you subtract 5 dollars with how much it Cost to make it which might be $1.50 so your profit will be $3.50. | You are starting a t-shirt business. It costs yo 5000 monthly for equipment an rental. And it costs $2.00 for supplies for each shirt. You sell each shirt for $7. Write your(a) cost function;(b) revenue function; and (d) estimate the number of shirts you have for sell in order to break even. | 1. You have to find the cost or c(x) which in this problem is c(x)=5000+2x. 2. Then you have to find the revenue or r(x) which is r(x)=7x 3. After that you have to find profit or p(x) which is p(x)=7x+(-5000-2x). 4. After you have solved that you have found the break even point which is 1000 shirts. | In a linear word problem the time always is x and the amount is always y. The differences between the fixed costs and the variable costs. | The linear word problems and business problems they were both quite easy to under stand . | I'm not at all confused with any of these concepts. | andreschavez80@yahoo.com | ||||

33 | 8/24/2013 22:45:16 | Che | Helena | 1st you put the situation into a linear equation by translating (week #, variable) like (x, y). You find the slope, the y-intercept, and you have your linear equation. Calculate how much of the variable would amount to at a given time from the problem. | Extrapolating means to extend the application by assuming that existing trends will continue. For example, Thomas is collecting stamps every week. Assuming it's always going to be the same amount of stamps every week, Thomas can calculate how many stamps Thomas's going to get at the end of some number of weeks. | Thomas collects stamps because they look great and he heard he could get money from selling them. He keeps a stamp album and hopes it'll make him rich one day. During the first week of the year, he had collected 30 stamps. By the 5th week of the year, he had collected 190 stamps. Assuming Thomas's stamp collecting follows a linear model, (a) write the linear equation to model the number of stamps he had collected, (b) calculate how many stamps Thomas had collected by week 4; and (c) predict how many total stamps Thomas will have collected by week 13, assuming this pattern continues. | First, you translate your variables into (week #, stamps collected). You would have gotten (1,30) and (5, 190). Now, from here, you solve for the slope getting 40. Plug your slope into the slope intercept form-> y=40x+b and solve for b. You would end up with (a) y=40x-10. To solve for (b), you would remember the number of weeks is equal to the 'x' variable prompting you to plug 4 weeks into the equation like so--> y= 40(4) -10. (b) is 150. The same goes for (c) in which you plug 13 weeks into x --> 40(13)-10. (c) is 510. | There are fixed costs and variable costs. Variable costs have a variable (x) with them and quantity is varied. Fixed costs are the same payments for every month. | Revenue is the money you charge. Profit is the money you get out of your revenue and cost. In real life, you want to sell bread in a bakery but you need to buy ingredients like flour and yeast. What happens is you buy your materials (variable cost) and then you sell your bread and you get money back (revenue). Your revenue with make up for the variable cost and the money left over will be your profit! | You are starting a bread bakery. It costs $1500 for monthly rent, and $8 for supplies. You sell a loaf of bread for $12 each. Write your (a) Cost Function; (b) Revenue Function; (c) Profit function; and (d) estimate the number of loaves of bread in order to break even (round up to the nearest loaf of bread if necessary and find the amount of profit if you do round up) | The first thing we have to find is the Cost Function which is made of of the Fixed and the Variable Costs. Your Fixed Cost is going to be the $1500 monthly rent added with your Variable Costs which will be $8. This makes your (a) Cost Function: C(x)= 1500 + 8x. Next, we find how much you are selling the bread, the Revenue. This makes the (b) Revenue Function: R(x)= 12x. Thirdly, the Profit Function is found when you subtract your cost function from you Revenue Function like --> R(x) - C(x). When you plug your functions in it should look like 12x-1500-8x but it isn't fully simplified so you add like terms and get your (c)Profit Function: P(x)= 4x-1500. Finally, we want to estimate how many loaves of bread we need to sell in order to break even and maybe get some profit left over. We solve our Profit Function: 4x-1500 --> 1500= 4x --> and find we need to sell (d) x= 375 loaves of bread. We did not need to round up so there is no profit from this sale. | x-value represents time & y-value represents amount Cost: C(x)= Fixed costs + Variable Costs(x) Revenue: R(x)= [how much you charge](x) Profit: R(x)- C(x) BEP: P(x) =0 / R(x) = C(x) | I thought there were both understandable. | Nothing seemed confusing to me. | helenache@hotmail.com | ||||

34 | 6/28/2013 22:31:31 | Chuong | Brian | The process of solving a linear model world problem begins with recognizing ordered pairs, proceeds with deriving the slope from the ordered pairs, continues with finding the b-value by using the equation together with an ordered pair, and ends with establishing the full equation. From there on, you can use the full equation to substitute in any values you want and find an output for them. | Extrapolating should mean assuming a point that was not given through logical reasoning. An example would be assuming that the point of (2,2) would be on a line that included the ordered pairs of (1,1) and (3,3). | Brian sells sugary confections in a cart on the boardwalk of some random beach. During week 1, he sells 0 sugary confections. During week 6, because of his apathetic attitude towards work, he sold 5 sugary confections. Assuming his sales follow a linear model, (a) Write the linear equation to model his sales; (b) calculate how many sugary confections Brian sold during week 2; and (c) predict how many sugary confections he will sell during week 182637287 if this pattern continues. | The ordered pairs we are given in said problem are: (1,0) and (6,5). By subtracting 5 by 0 and dividing it by the subtraction of 6 by 1, we are given 5 over 5, which would make the slope of the linear model, 1. If we substitute in the first ordered pair to make 0 = 1 (1) + b, and continue on to simplify the equation to 0 = 1 + b, we arrive at the end result, which would be b = -1. With this, we are given the b-value, and obtain the full equation, which would be y = x - 1. If we substitute 2 in for x, we arrive at y = (2) - 1, which can be simplified in order to reach the end result of y = 1, making his sales at week 2 be 1 sugary confection. If we substitute in 182637287 for x, we arrive at y = (182637287) - 1, which can be simplified in order to reach the end result of y = 182637286, making his sales at week 182637287 be 182637286 sugary confections. | The two different types of costs that we have are fixed costs and variable costs. Fixed costs are basically costs that are absolute/definite within a given time period, and variable costs are costs that are dependent upon one or more variables that, in the end, will give you the final cost. | Revenue is basically all of the earnings that you had made. Profit is also how much you had made, but deducting how much you had spent in order to earn that much in as well. For example, let's say that I had raked in $50 from selling lemonade, but beforehand, I had spent $20 on the supplies that I needed in order to sell lemonade, making my actual earnings only $30. In that example, that $50 would be the my revenue, but my profits would only be $30 of that $50. | Brian is starting his own sugary confection business. It costs him $1 for monthly equipment and rental fees, and $1 for supplies for each sugary confection. He sells each sugary confection for $182637287. Write your (a) Cost Function; (b) Revenue Function; (c) Profit Function; and (d) estimate the number of sugary confections he will have to sell in order to break even (round up to the nearest sugary confection if necessary &tell how much profit you will make if you have to round up). | The cost function for said Cost-Revenue-Profit word problem would be C(x) = 1 + x. The revenue function for said Cost-Revenue-Profit word problem would be R(x) = 182637287x. The profit function for said Cost-Revenue-Profit word problem would have to be derived from subtracting the cost function (C(x) = 1 + x) from the revenue function (R(x) = 182637287x), which would be P(x) = 182637286x - 1. To find how many sugary confections Brian would have to sell in order to break even, we would have to set the profit function (P(x) = 182637286x - 1) to 0. From there on out, we would then proceed to add 1 to each side to make P(x) = 182637286x = 1, and would then divide 1 by 182637286 in order to get x = .00000000547533322412598706706581261835, which we would round to 1. In order to find his profit from selling 1 in order to break even, we would have to set up the equation of P(x) = 182637286(1) - 1, which we would proceed to simplify to 182637286 - 1, which would then equal $182637285 or profit. | None, really. | All of it. | None of it. | chuongbrian@gmail.com | ||||

35 | 8/27/2013 1:07:03 | Contreras | edgar | first you have to get 2 sets of ordered pairs, the x value represents the time and the y value represents the amount. then you plug that in to the given equations. | it means predicting future outcomes out of results you have already obtained. | Aiden just started a modeling company and is helping sell clothing at a local store. by the end of two weeks sales had gone up 20 extra pieces of clothing sold than usual. by the end 6 weeks the store sold around 80 more pieces of clothing than they normally would have. | First we find our two ordered pairs (2,20) (6,80.) then we use y2-y1/x2-x1; which equals 15. then you choose one ordered pair and plug it in to slope-intercept form. 20=15(2)+b, b=-10. | The two types costs we have are fixed cost and variable costs. Fixed costs are paid monthly and doesn't not increase. Variable costs is how much money you make every month. | The difference between revenue and and profit is how much money you charge and revenue is the money you make . For example if your sell a sweater for 30 dollars, you make 25 dollars because it costs you 5 dollars to make the sweater. | Aiden recently started a modeling company it costs him $40 for equipment and $20 to hire a model for a shoot. but Aiden gets paid $35 for each cover. | step 1, we find the cost which is 40+20x. then we find the revenue; r(x)=35x. and our prophit would come out to be p(x)=15x-40. our breaking point will end up as x=2.67. and our profit end up at a little $.05. | the most important terms to remember are the key words, such as; breaking point, BEP, revenue and remembering that you have to plug it in correctly in the right place. | what i understood the most was the Business problem part, it seemed logical and easy to understand. | i still get confused when trying to finish a linear model. I dont know why but i seem to forget where you are suppose to put each variable/number in the equation | du.de_777@yahoo.com | ||||

36 | 6/28/2013 22:06:33 | cruz | Selene | In order to solve a linear model you have to find your ordered pairs. You then find your slope and then plug it back into y=mx+b to find your y-intercept. With that information you can write your linear equation and plug in whatever number the problem gave you to calculate. | Extrapolate means to estimate something (distance, numbers, patterns etc.) based on given information. For example, if you have if you have ordered pairs, (1,1) (1,2) (1,3), you can extrapolate that the next one would be (1,4) | Leah sells home made bracelets. During her first week she sold 13 bracelets. During her fourth week she sold 38 bracelets. Assuming her sales follow a linear model, write a linear equation, predict how many bracelets she is going to sell on the 8th week and10th week? | Your ordered pairs would be (1,13) (6,38). Use the slope formula to find your slope. Then, use one of your ordered pairs and your slope to plug back into y=mx+b to find your y-intercept. Once you have your y-intercept and slope write a linear equation. Finally, plug in 8 and 10, those are the weeks they want you to predict, into your linear equation and you will have your two answers. | The two type of costs are, fixed costs and variable costs. Fixed costs are things you pay monthly and you pay about the same amount each month. Variable costs vary from moth to month depending on how much of something you decide to produce and spend. | Revenue is how much something is sold for and profit is how much u make after the sale. Lets say im selling a shirt for $12 but I bought it for $6. So my profit would be $6. | Leah sells home made bracelets. It costs her $1500 for monthly equipments and rental fees, and $.50 for the supplies needed to make the bracelets. You sell each bracelet for $.75 Write the cost function, revenue function, profit function, and estimate the number of bracelets you will sell in order break-even. | You need to find the cost function, revenue function, profit function, and estimate the break even point. Your cost function would be 1500+.50x. Your revenue profit would be .75x. Next, you need to find your profit function, you combine you cost function and your revenue function to find it. So it would be .75x-(1500+.50x), you need to distribute the negative sign and combine like terms, your final function would be .25x-1500. You then need to set the profit function equal to zero and solve for x and that is going to be your answer. | I think the most important term to remember is extrapolate. Im sure we will continue using this word through out the year. I think it would also be useful to remember the two different type of costs there is. | I understood how to write linear models the most. We just recently reviewed how to find slope so it was still fresh in my mind. That helped me understand the concept more. | Im still confused about the cost, profit, and revenue word problems. Im only confused on the break even point. I understand how to solve the problem, I find it similar to the linear model word problems, I just dont understand what the difference is between break even point and profit. | selenecrz21@yahoo.com | ||||

37 | 6/26/2013 15:49:35 | Cuevas | Fabiola | To solve a linear model word problem you must make two sets of ordered pairs using the times and amounts given to you. Time is always the x-value and the amount is the y-value. With these two ordered pairs you plug them into the slope formula. You then plug an ordered pair and the slope into the slope-intercept form to find b. When you have found b you have your equation. If you are told to find the amount for another set of time you extrapolate the line you already have with the original first two points to find the answer. To find the answer you plug it into your equation. | Extrapolating means to predict a number outside of the points you are given using the pattern from those to points. For example if you sell 4 apples in one week and in 6 week you sell 34 apples and you are asked to find how many apples would be sold in 15 weeks, you would find a pattern between those two points and use it to estimate the number of apples sold in 15 weeks. | Sally started selling knitted bracelets during the summer. In her first week she sold 8 bracelets. During week 5 she had sold a total of 48 bracelets. Assuming her bracelet sales follow a linear model, (a Write the linear equation to model her total sales; (b) calculate how many bracelets Sally would have sold by the 3rd week; and (c) predict how many total bracelets will have sold by the 50th week if this pattern continues. | The weeks are the x-values and the number of bracelets sold are the y-values. In her first week Sally sold 8 bracelets so the ordered pair would be (1,8). In her 5th week she sold 48 bracelets which translates into (5,48). The first thing you need to find is the linear equation given two points. Plug the 2 points into the slope formula to get (ysub2)48-(ysub1)8 over (xsub2)5-(xsub1)1=40 over 4=10. You plug the slope (10) as well as one of the original points into y=mx+b. I will plug in the smaller point to get 8=10(1)+b. You subtract 10 on both sides and b=-2. The linear equation would be y=10x-2. For b you plug in 3 for x. y=10(3)-2=30-2=28 bracelets sold in the third week. For c you plug 50 into the x. y=10(50)-2==500-2=498 bracelets sold in 50 weeks. | The two types of costs are fixed costs and variable costs. These two are similar in that they both reduce the profit made. Fixed costs don't really change every month and are costs from rent, electricity,etc. On the other hand, variable costs are the amount of money it takes to make the item and vary each month depending on how many items you make each month. | Revenue is the amount of money you charge for your item while profit is how much you actually make once you subtract the money you spent making the item. For example if you sell 50 $13 shorts in a month,in which case $13 would be the revenue, making a total of $650 but you spent $620 making the shorts your total profit is only $30. | Sally decided to expand her knitted bracelets business. She pays $1300 for monthly equipment and rental fees, and$ 0.50 for supplies for a bracelet. She sells each bracelet for $5. Write her (a) Cost Function; (b) Revenue Function; (c) Profit Function; and (d) estimate the number of bracelets she will have to sell in order to break even (round up to the nearest bracelet if necessary and find the amount of profit if you do round up.) | To find the cost function you add the fixed cost with the variable costs(x). The fixed cost in Sally's situation is $1300 and the variable cost is $0.50. The Cost Function C(x)=1300+0.5x. The revenue function is just the amount you sell the item for and an x after it. The Revenue Function for the bracelets is R(x)=5x. To find the profit function you subtract the revenue function with the cost function. The Profit Function is P(x)=5x-(1300+0.5x)=5x-1300-0.5x. P(x)=4.5x-1300. To find the break-even point you set the profit function equal to zero. 4.5x-1300=0 add 1300 to both sides to get 4.5x=1300 then divide by 4.5 on both sides. The BEP is 288.89 which rounds up to 289. Since we rounded up we have to find the profit Sally would make. To do this you plug the BEP into the profit function. P(289)=4.5(289)-1300=1300.5-1300=.5. Sally's profit would be 50cents. | extrapolate, linear model, equations for cost, revenue, profit, and BEP | solving for cost, revenue, and profit functions. | finding the BEP or profit after you have found the BEP. | fabycuevas18@yahoo.com | ||||

38 | 6/29/2013 13:43:54 | De La Rosa | Lucero | You have to first write down the important information in standard form (x,y) (x,y)by representing the x's as your time and the y's as your amount. After, you need to find your slope so your equation will be (y2-y1)/(x2-x1). Then you pick any of your two original equations and plug it in into y=mx+b. Then you find what exactly is the equation asking for and plug in the week, month(etc.) as the x in your new equation that is written in the form as y=mx+b. | Extrapolate means make more of or simply expand. For example if you read a book and every week you read more and more pages, you can calculate how many pages you read from your first week of reading to (let's say) your 8th week of reading and find out the page numbers you read and will continue to read in the 37th week (of course there is no book that is that long except for maybe the bible but this is an example so that's ok). | April enjoys working out during the weekend. On her first week she realized she lost 2 pounds and on her 7th week she realized she had lost 20 pounds.(a.)Write the linear model to show her progress; (b.) calculate how many pounds she lost on week 3; (c.) predict how many pounds she will lose during week 12. | You have to first write down the important information in standard form (x,y) (x,y)by representing the x's as your time and the y's as your amount. The numbers are (1,2)(7,20) After, you need to find your slope so your equation which in this case will be (y2-y1)/(x2-x1). So now you have to plug in the numbers (20-2)/(7-1). Your answer will be 18/6 but since you can cimplify this, your answer is 3. Then you pick any of your two original equations and plug it in into y=mx+b. I chose (1,2) so now i have to plug it in; 2(y)=3(m) x 1(x) =b. 3 x 1= 3 so it ends up being 2=3=b. Now we need to subtract 3 from both sides and we end up getting -1. Now you can plug it in into y=mx=b which is y=3x-1. Then you find what exactly is the equation asking for and plug in the week, month(etc.) as the x in your new equation that is written in the form as y=mx+b. Since they are asking for week 3, we plug that number as our x into our new equation. y=3(3)-1 which equals 8. That means April lost 8 pounds on week 3. The last thing they are asking for is to find out how many pounds she will lose in week 12. We then plug in that number to our equation. y=3(12)-1 and solve. We get 35. That means April will lose 35 pounds in week 12. | Fixed costs and variable costs(always have a variable costs usually x). Fix costs are things you pay monthly such as rent and car prices. Variable costs depend on how many items you make such as if you make different kinds of sweaters in different colors and sizes. All your shoes are not going to cost the same for various reasons. | Revenue is how much you charge someone depending on the different item you sell. If you sell cats for $30 then your revenue is...$30. Profit is what is left over after you ay all your bills. If you have $300 to spend but $250 is for your brand new car, you are left with $50 and that is your total profit. | April is starting a nutrition business. It costs her $1800 for monthly equipment and fees, and $6.00 for supply for each fruit shake. She sells fruit shakes for $3.00. Write her (a) cost function; (b) revenue function; (c) profit function; and (d) estimate the number of fruit shakes she will have to sell in order to break even (round up to the nearest fruit shake if necessary and find the profit if you round up.) | You have to find the fixed cost which equals $1800 and the variable which costs $6.00. So the coss will be c(x)=1800=6.00. Then you have to find the revenue which is $3 per fruit shake. So the revenue = 3x. Next you need to know the profit which will be 3x-(1800+6.00x). Be careful because this is not your equation, you still need to simplify the negative which will be: -1800+3x. Now you need to find the break even point so we equal our answer to 0. 0=-1800+3x and add 1800 to both sides which is 1800=3x. Then you divide both sides by 3 which is 600. So you would need to sell 600 fruit shakes. | The key terms extrapolate and revenue are some key terms that help me a lot with these type of problems. | The problem I understood and sort of enjoyed doing is writing linear models and evaluating for word problems. | The concept that is still very confusing is the writing and solving cost, profit, and revenue word problems. I get the first part of the equation but I get lost as soon as we begin to solve for the profit. | lucero.delarosa@yahoo.com | ||||

39 | 8/13/2013 16:38:12 | de Leon | William | First you have to set up two ordered pairs. With those pairs you have to find the slope which will represent the change in the model. That slope is plugged in to the slope intercept formula along with two points from the ordered pairs. with that you can find what the y-intercept is. Later you just have to plug in the time that's being asked in the problem into x. With that you will be able to find out the factor that's being asked. | What extrapolating means is to extend. We know what happens at point one and at point 7 but we want to know what happens at point 12 so we extrapolate by following the pattern between 1 and 7 in order to find out 12 even if 12 was never mentioned. | Marty has decided to learn as many songs as possible in the guitar during the summer to impress his girlfriend. During the first week of summer he managed to learn 3 songs. By the 4th week of summer, Marty has learned 16 songs in the guitar. Assuming his completion of problems follow a linear model, (a) write a linear equation: (b) calculate how many songs he had learned by week 3; and (c) predict how many songs marty will have learned by the end of the summer (10 weeks). | First create the ordered pairs (1,3) (4,16), then find the slope of the problem. plug in the slope to the slope intercept formula. with that figure out what the y-intercept is. Using that formula plug in 3 and 10 each on a separate problem in order to find the amount of songs learned during that time period. | Fixed Costs: the fixed costs are the kind of costs that will not change. For example rent. Variable Costs: these are the cost that, as described on the word, VARY. These costs mostly depend of the product made and sold in the past period which will depend on how much profit has been made which implies how much should be spend the next time period. this is not always the same. | The revenue is the exact money that is given to you when someone buys something. A big mac is $ 4 The profit is what the person selling the product makes without counting what was used in order to make the product or the fixed costs. the person only keeps 2 dollars of each big mac. | Marty started his own Guitar lesson business. It costs $2000 to rent the place where he will be teaching his lessons, he spends $5 on booklets that he will hand out to the students. Every student has to pay $30 dollars per moth. write (a)cost function; (b)revenue function,(c)product function;(d)and estimate the number of students that he will have to teach in order to break even. | First find the cost function by following Fixed cost + variable costs(x) then find the revenue function by plugging in 30(x) then subtract the the cost function from the revenue function to find the profit function. equal the profit function to 0 to find the amount of students needed for BEP. | Extrapolate, cost, revenue, profit, Break-even point (BEP) | The Business problems | NONE | dwilliamjosue@live.com | ||||

40 | 6/19/2013 15:29:49 | Del Campo | Kelsea | To solve a "linear model" word problem, first you must read through the problem and find two x-values and two y-values. The x-values will represent time and the y-value will represent the amount. After finding the x-values and y-values, you use the slope formula to find the slope. After doing that, you use the slope-intercept formula and plug in the numbers to find the y-intercept, or b. After finding b, plug in m and b to the slope-intercept formula. | The word extrapolating means to predict what will happen. For example, if we were given a problem that told us about a bow company selling three bows their first week and thirty bows their fifth week, we can make a linear equation, assuming her sales follow a linear model. However, if we want to know how many bows they will sell their tenth week, we will use the linear equation and extrapolate. | Lauren has an obsession with bows. She decided to make her own bows, open a website, and sell them. During week one, she sells five bows. During week 6, since bows became more popular, she sold 45 bows. Assuming her sales follow a linear model, (a) Write a linear equation to model her sales; (b) calculate how many bows sally sold during week 5; and (c) predict how many bows she will sell during week 20 if this pattern continues. | First, read through the problem and find the x-values, the time, in this case the week, and find the corresponding y-value, the amount sold that week. The points will be (1,5) and (6,45). For part (a), use the slope formula to find the slope. So the equation will be 45-5/6-1=40/5=8. Once the slope is found, use the slope-intercept formula to find b, the y-intercept. You can choose any x and y pair. So the equation will look like this: 5=(8)(1)+b. That will simplify to b= -3. Then, plug m and b in to the slope-intercept formula. The equation will now look like this f(x)=8x-3. To find part (b), use the formula we just found, f(x)=8x-3, and plug in 5 where the x's are. f(5)=(8)(5)-3=40-3=37 bows. For part (c), we do the same thing s part (b) but plug in 20 instead. f(20)=(8)(20)-3=160-3=157 bows. | There are fixed costs and variable costs. The fixed costs are consistent monthly payments to monthly equipment and rental fees. Variable costs are not consistent and is the amount it costs to make each item. Both are payments, however, ones is consistent and the other is not consistent. | Revenue is how much each item you are selling costs. Profit is the amount of money you actually make after paying rent, the equipment, and the item. For example, if you were to open business, y would need to pay rent, buy equipment, and buy the actual product. To make a profit, you would need to sell the item for a certain amount of money so that if enough items are sold, you can pay rent, pay for equipment, pay back the company that provided the item you are selling, and provide for yourself. | Lauren is moving her online store to an actual shop. Its costs her $1300 for rental fees and monthly equipment, and $1.50 for supplies for each bow. Lauren sells each bow for $4.00. Write your 9a) Cost functions; (b) Revenue functions; (c) Profit functions; and (d) estimate the number of bows Lauren will have to sell in order to break even (round up to the nearest bow if necessary and find the amount of profit if you do round up.) | For (a), to find the cost profit, we need the fixed costs and variable costs. Those are the rental and equipment fees and the supplies it takes to make each bow. Once you find them, you must use the equation C(x)= fixed costs + variable costs (x). The equation is now 1300+1.5x. To find (b), the revenue function costs, just use the equation R(x)=__(x), the blank space is the amount each bow costs. That makes the revenue functions R(x)=4x. To find (c), the profit functions, use the equation p(x)=revenue function - cost functions. That makes the profit functions P(x)=4x-(1300+1.5x). Simplified it would be P(x)=3.5x-1300. Lastly, for (d), to estimate the break point, we just need to equal the profit function to 0. 3.5x-1300=0. Then simplify it by subtracting 1300 to both sides then dividing by 3.5. That makes it 371.4, but we need to round up, so it will be 372. Since we rounded, we need to find out how much profit she made since we rounded, so we use the profit function equation. P(372)=3.5(372)-1300. Simplified, she makes $2, just passed her break even point. | the equations and how to carefully analyze each word problem. | how to find the linear equation and all the equations involved with business problems. | break even point. | lilxkelsea@yahoo.com | ||||

41 | 6/28/2013 15:13:34 | Dominguez | Patricia | to solve a linear model you fist need to find the x value which is the time and you need too find the y value which is the amount. After you find the time you started and the amount you started with you make a pair of numbers. then you read and you find the second pair of numbers being the last amount and the last time. you grab those to set of pairs and you find the slope between them. after you find the slope you use a set of numbers and solve the equation y=mx +b. after you find the answer to b you have come to your complete equation. | the word extrapolating means to predict. for example you need to predict what amount of work you will have done after the end of summer. | billy sells starfish on the weekends. During week 1, he sold 4 starfish. During week 2, he sold 12 starfish. Assuming his selling follows a linear model, (a) write the linear equation ;(b) calculate how many starfish did he sell by week 7 ; and (c) predict how many he will sell by week 24. | first we will find the equation of the problem. we will grab 12-4/ 2-1 which we will get 8. After we find the slope we plug it in to y=mx+b form. We will use the first set of numbers (1,4) we will plug it in to have an equation looking like y=8x-4. We will plug in y=8(7)-4 our answer being 52 starfish. then we will predict how many we will have by week 24. y=8(24)-4 we get 188 starfish. | we have two different type of cost. we have the fixed cost and the variable cost. the fixed cost is what a person pays monthly like bills ,rent etc. Variable cost is how much it costs a person to make a certain thing. | the difference between revenue and profit is that revenue is the amount a person charges or ask for,for an object. profit is what you of the object being sol or the left over money after you have payed all the fixed cost. | Billy started selling starfish. It costs 1200 a month of equipment and rental fees, and it cost $.50 for the starfish. if he sells every starfish for $.75. (a) cost function; (b) revenue function ; (c) profit function ; (d) estimate the number of starfish billy will sell to break even. | first we will find the equation. a) c(x)1200+$.50 then we will find the revenue function being the amount you are selling for. b) r(x).75x after we will find the profit c) P(x)= .75x-(1200+.50x) we distribute the negative and we get 0.75x-1200-.50 if we combine like terms we get 0.25x-1200 we must then find the number of starfish to break even so we equal it to 0 0.25x=1200 we divide by 0.25 and x=4800 since the number doesnt have decimals we do not need to round or find the amount he will need to break even only because it doesnt have a decimal. | how to write a linear model and how to evaluate it and how to solve cost, profit, and revenue word problems | is how to sold linear models | n/a | patricia.dominguez1@yahoo.com | ||||

42 | 8/23/2013 0:34:40 | Drayton | Kenari | 1. Find the slope of the linear model by determining the x and y- value 2 Using the slope write a linear equation to model the word problem 3. Plug in the x-value to get an output for the y-value | Extrapolate is used when a linear model is assumed. Extrapolating would be used when trying to figure out info ahead of the points you have plotted. For example, if I plot the points (2,1) and (5,3) I would extrapolate by continuing the plotted points. | Ty owns a tie business and sells them online. His first week he sells 7 ties. By the 7th week he sold a total of 55 ties. (a) write a linear equation to model his total tie sales (b) calculate how many ties he sold during the 3rd week (c) predict how many ties he will sell during his 11th week, if the pattern continues. | The x-value of a linear model always represents time and the y- value always represents an amount. Thus, my points are (1, 7) and (7, 55). Iwould have to find the slope using these two points which is 8. Then I would use the slope to find the linear equation by plugging in an x- value. 7=8(1) +b and b = -1. The answer to part (a) is y=8x-1 To solve for part b, I would then plug in a 3 to represent the 3rd week. 8(3)-1= 23 and my answer is 23 To solve for part c, I would plug in the number 11 to represent the 11th week. 8(11)-1=87 and my final answer is 87 | There are two types of costs which are fixed costs and variable costs. Fixed costs are usually paid monthly and stay the same about every month. Variable costs differ because it is the cost to make each item being sold. These costs vary monthly based on how many items are produced. | Revenue is the total amount for how much you charge for each item sold. Profit is how much money is actually made because you must subtract your costs from your revenue. For example, if it costs me $3 to make a bracelet but I sell 10 for $5, my revenue is $50 dollars because that is how much money which was brought in. However my profit would be less than that because I still would have to subtract $30 for the costs that it took me to make the bracelets to sell leaving me with a profit of $20. | Ty decided to buy a location in his neighborhood to expand his tie business. It costs $1400 in monthly fees, and $3 for supplies for each tie. He sells each tie for $7. Write your (a) cost function; (b) revenue function; (c) profit function; (d)estimate the number of ties he will have to sell in order to break even | First I must write my cost function which is 1400+3x because my fixed cost is $1400 and my variable cost is $3. (a) c(x)=1400+3x Ty is charging $7 per tie so my revenue function is 7x (b) R(x)=7x I must subtract the costs from the revenues to determine the profit made. (7x)- (1400+3x) which becomes px=4x-1400 (c) P(x)= 4x-1400 In order to solve the break even point I must set the equation equal to zero. 0=4x-1400 1. Add 1400 to both sides Then you get 1400= 4x 2. Divide by 4 1400/4 =350 (d) BEP must be 350 | The most important key facts I need to remember are the difference between the fixed and variable costs. | The part I understood most from the two concepts was the difference between revenue and profit. | I am not confused on these two topics. | dr8on28@gmail.com | ||||

43 | 6/26/2013 22:24:45 | Duong | Annie | The first step to solving a linear model problem is transforming the given information into two coordinate points. Make sure first to see if the problem tells you if the current situation is growing in a linear pattern. Now you need to find your x and y values. To find the x values, look for a measurement of time (like weeks, days, hours, etc.) and to find the y values, look for the amount created over that certain period of time. The next step is to create the equation. Find the slope by using the classic formula of y2-y1/x2-x1! Once you have the slope, you can find the y-intercept by simply plugging back in a point you created in the previous step. (Use the smaller numbers so you won't have to suffer!) After you find the equation then you can solve anything that the problem asks you. For instance, you can find the amount of after 10235 days by simply plugging 10235 as the x-value. You can plug the numbers back in to check your work. And you have solved the problem! | Extrapolating means to extend a piece of given information in order to infer or correctly estimate something. For example, if you have two coordinate points and you graph them on a graph and draw a line connecting them, you can figure out even more points on that line if you were to extend it in the same direction. For this particular example, you can only do so if the equation follows a linear path. | Philtrum is a firm animal rights activist. He is particularly interested in saving as many turtles living in environments that cause them harm. His goal is to gather as many as possible and distribute them to areas where they are safe such as their natural habitats or reptile houses. On the first week of his adventure, he goes to Alaska and finds 3 turtles shivering in the cold. During the 6th week, Philtrum went to Costa Rica and found 28 turtles sweltering in the hot sun. Assuming his turtle collecting follows a linear model, (a) write the linear equation to model the number of turtles he has collected, (b) calculate how many turtles he collected by week 4, and (c) predict how many total turtles he will have collected by week 14. | It is vital that we help those turtles in need. The most that we can do is to solve those problems! First, we need to determine if this is a linear model problem. Since it says so in the 5th sentence, we can assume this. First, we have to find our coordinate points by determining the x and y values. The x values in this case is the number of weeks and the y values is the number of turtles collected. We can write the first week as (1,3) because 1 is the first week and three is the number of turtles collected. The other coordinate can be written as (6, 28) because 6 represents the week number and 28 is the number of turtles collected. Then, find the slope by using the slope formula. Write (28-3)/(6-1) and solve to get 5. Once you get your slope, figure out the slope-intercept (b) by plugging in one of the known coordinates. Use (1,3) because it is easier. Your final answer should by y=5x-2. To solve (b), know that the problem gives us the x-value because it is a measurement of time. We can now plug the number 4 into our formula and solve for the number of turtles collected during that week. Use PEMDAS to solve the equation and your answer should be 18 turtles. The last step is to solve for (c). To do this, simply plug in the number 14 into “x”, follow PEMDAS and solve! Your final answer should be 68 turtles. Always remember label your answers with the correct units. | We have two different types of costs: the fixed costs and the variable costs. What makes these two different is that fixed costs are costs that stay the same about every month and are paid monthly. These costs are, hence their name, fixed. Some examples included the rent for an apartment, advertising, or utilities. Variable costs are the amount of money it takes to create or obtain an item intended for profit. These costs vary monthly based on how many items the seller decides to produce. Examples of variable costs are paying pencils intended to be sold later on for profit and books intended to be sold later in a bookstore. These costs are similar in that they both determine how much money is needed to pay for the business venture. | The difference between revenue and profit is that revenue is the amount of money charged for each item sold while profit is the amount of money made by selling that item at a price higher than its original cost. For example, say we have a business that involves selling teddy bears. We first have to buy the teddy bears from the manufacturer. For instance, one teddy bear may be $5. This is our revenue. When we sell at the shop, the teddy bears are sold for $8. When we subtract the revenue from the price we sold the teddy bears, we get $3, which is our profit. In order for a business to be extremely successful, much profit must be made. | Yeye is starting his turtle accessory business. These accessories are shaped like miniature turtles with engraved messages that encourage environmentally friendly habits. It costs him $2000 for monthly rentals for the shop and $1.50 for each turtle accessory. He sells each accessory for $3.50. Write the (a) Cost Function, (b) revenue function, (c) profit function, and (d) estimate the number of accessories he would have to sell in order to break even. (round up to the nearest accessory necessary and find the amount of profit if you do round up). | First, let us determine the cost function. All the cost function is adding the fixed costs to the variable costs. The fixed costs would be something that is paid monthly, so in this example, the $2000 is our fixed costs. The variable costs would be how much money it takes to make each item so the $1.50 would be the variable cost. When we write the variable cost, an “x” or some sort of variable must be multiplied to it to indicate the number of items being sold. Write your answer like so: 2000 + 1.5x . To find out the revenue function, simply take the amount of money you are going to sell the accessory ($3.50) and multiply by x, because this will determine how many accessories you actually sold. Your answer should be 3.5x. To determine the profit function, take your cost function and subtract it from your revenue cost. Be careful here since the cost function has two parts to it. Put parentheses around the cost function before subtracting to make your life easier. Write it like so: 3.5x – (2000 +1.5x). Make sure to distribute the negative to the cost function and combine like terms. Your answer should be 2x – 2000. To determine the amount of accessories needed to find the break-even point. There are two ways to do this: setting the profit function to zero or setting the revenue function and cost function equal to each other. Let’s set the profit function to zero for the easier way. 2x – 2000 = 0. Add 2000 to both sides. The new function is 2x = 2000. Divide 2 to both sides and your answer is 1000 accessories. This is your break-even point. To determine the profit, plug in your break even point (1000) into the profit function formula. 2(1000) – 2000. Multiply 2 by 1000 to get 2000 and subtract 2000. Your answer is 0, meaning that you made no profit at all. | •extrapolating •linear models •cost •revenue •profit •break-even point | how to write and solve a linear model equation and how to accurately predict a linear pattern and the basics of business economics. For instance, the difference between revenue and profit. | the significance of the break-even point and how it contributes to success in business. | duong.annie@ymail.com | ||||

44 | 6/27/2013 22:20:07 | Eggers | Bianca | First, one needs to see the first week and how many items are collected or sold, this will go in the first coordinates. Next, one will look at the second week and see how many items are sold and this will go in the second coordinate. Once the numbers are put in the coordinates, one will need to plug in the x and y coordinates into y2-y1 over x2-x1. This is the formula to get the slope, once one gets the slope they will plug in one coordinate pair for x and y in y=mx+b. Then, one needs to put the answer into f(x) form. Such as f(x)= 5x+4. | To extrapolate means to extend the linear graph/equation. | Carla sells designer shoes at Nordstrom. During the 1rst week she sells five pairs of designer sandles. By the sixth week she sold 45 pairs. Assuming her sales follow a linear model, a) Write a linear equation to model her sales; b) caculate how many shoes Carla sold during week three. c) predict how many she will sell in week 7. | First I will put the 1 for the x in the 1rst coordinate and 5 for y. Next, I will put 6 for x in the second coordinate and 45 for y. Then, I will plug this into y2-y1 over x2-x1 and solve. Once, I have the slope which is 8, i will plug it into y=mx+b and plug in the coordinate (1,5) for x and y. Then the answer for a) is f(x)= 8x-3. To solve for b) I will need to put f(3) which means to plug in three for x in the equation. 8(3) -3 is 21, Carla sold 21 designer shoes in week 3. Lastly to solve for c) one will plug in 7 for x in the equation, resulting in 8(7) -3 is 51 shoes. | The first cost is fixed cost which means these cost do not change such as needing to pay for a water bill. The next cost is Variable cost which does change and varies in cost each month. | Revenue is how much one charges for thier product. For instance, Starbucks sells their Frappachinos for $4 for a tall. While, a Profit is money that is earned such as Starbucks earns more money if more people buy from their store than Coffee Bean. | My sister started a new clothing store. It costs her $2000 for monthly equitment and rental fees, and $.75 for each piece of clothing. She sells each piece of clothing for $5. a) Her Cost function. b) Revenue function and c) Profit function and d) she will need to estimate the number of clothes she wil need to sell in order to break even. | First, the cost is C(x)= 2000+ .75x. Revenue is R(x) = 5x , Profit is P(x) = 5x- (2000+ .75x), distribute the negative to 2000 and .75. Which gives my sister 4.25x- 2000. However, we need to find d) which is BEP so we must put 4.25x- 2000 equal to 0. Then, subtract 2000 and divide 4.25 to get x= 480 pieces of clothing. | the equations for Cost, Revenue, Profit and BEP. | that Profit is the money you make, while Revenue is how much you sell the product for. Also, I realized knowing the equations to solve word problems is critical. | I am not confused about any concept. | eggers_bianca@yahoo.com | ||||

45 | 8/20/2013 16:02:43 | Elias | Mia | To solve a "linear model" word problem you must first set up the two ordered pairs and plug them into the slope formula. Then you use that formula and one ordered pair and plug those in to Y = mx + b to get b. After getting the linear equation, we can plug in any week to find the number of objects asked for. | Extrapolate basically means to extend the line past the already given range, assuming that it continues to follow a linear model. For example, in linear model problems, we must extrapolate the line to get an approximation of a future number. | Elina loves nothing more than to read. After the first week of her school year she read three books. By week six, she read a total of 52 books. Assuming her reading follows a linear model, (a) Write the linear equation to model how many books she has read; (b) calculate how many she read by week four, and (c) predict how many books she will have read by week 23. | First you must get the two ordered pairs which are: (1,3) and (6,52). Then we plug these sets into the m = Y2 a Y1/ X2 - X1 formula to get the slope. Next, we use one of the ordered pairs with the slope to find b; together they form the linear equation: Y = 49/5x - 34/5. Finally, to know how many books she were to have sold during week 4 and week 23, plug in 4 and 23 as the values of the linear equation. Y | The two different types of costs are Fixed Costs and Variable Costs. The fixed costs are paid monthly at approximately the same amount ever time. An example of a fixed cost is rent. The Variable costs, however, change depending on how much or how many of the product is sold; no month is ever the same. | Revenue is the amount a business person charges for every one of their product. The purpose of revenue is to pay back the costs needed to make the product. Whatever is left over after covering the cost is the money made for ourselves, also known as Profit. | Elina is starting her own bookstore. It costs her $1250 for monthly equipment and rental fees, and $1.75 for each book. She sells each book for $4.99. Write her (a) Cost Function; (b) Revenue Function; (c) Profit Function;and (d) estimate the number of books she will have to sell in order to break even (round up the nearest book if necessary and find the amount of profit if you do round up.) | A. $1250 + $1.275x is the cost, B. $4.99x is the revenue. C. The profit is the revenue less the cost which in this case will be 3.24x - 1250. Next set the profit function equal to zero and simplify: 3.24x = 1250, divide both sides by 3.24 to find that in order for Elina to break even she must sell 386 books. The profit is $.64. | The most important facts to remember are the different numbers found in business problems. Also, that when ever the BEP is left at a decimal, it is mandatory to round up one because an object cannot be sold in portions. | The part I understood most is in concept six when we basically focus on getting the linear equation and then simply plugging in other numbers. | In concept seven, it is easy to get confused because there are so many different factors that represent completely different things. Sometimes I get lost when trying to find the complete profit because we have to round. | miaaelias1 | ||||

46 | 6/28/2013 17:27:16 | Escoto | Arely | First you have to find the two ordered pairs given in the backstory and find if it is a problem that follows a linear model. Next, you use the equation to find the slope of the two ordered pairs. After that you plug in the known numbers into the slope-intercept equation to find "b", the y-intercept. Finally, you plug in the week number into the X to find the amount of items attained. | Finding the missing answers with the answers or work you already have. An example would be if you have 3 points on a line and you need to find the 75th point, you use what you have to figure it out. | Leonard McCoy is a new medical biologist and is breeding small alien bunnies called Tribbles. Tribbles reproduce at an amazingly rapid pace. In week one, one Tribble produces 3 offspring. By the end of week 5, one single Tribble produced 25 offspring. Assuming their breeding patterns follow a linear model, (a) write the linear equation to model the number of offspring produced on week 9 and (c) predict how many offspring will be produced after week 18, assuming the patten continues. | Step 1) First you acquire the information from the text. Step 2) Figure out the two ordered pairs and use them to find the slope by using the slope formula. Step 3) Plug in the slope into the slope-intercept equation; M being the slope and use one of the equations to plug in as X and Y. Step 4) Using the week number given in the equation plug it in to f(x) and solve. Step 5) Put a square around the answer and that is it. | The two different types of costs are fixed costs and variable costs. Fixed costs is an amount of money that has to be paid monthly and it can include the rent and the utilities and the variable costs are how much it is going to cost to make an item, and this cost changes depending on how many items are made each month. | Revenue is how much you charge for each item you sell, while profit is how much money you make for yourself after subtracting the fixed and variable costs. | After breeding all the Tribbles, Leonard McCoy wants to open up McCoy Pet Store to sell the Tribbles and make a profit. It will cost McCoy $1300 for monthly equipment and rental fees, and $5 to buy the supplies for each Tribble. He will sell each Tribble for $15. Write your (a) Cost Function; (b) Revenue Function; (c) Profit Function; and (d) estimate the number of Tribbles McCoy would have to sell to break even (round up to the nearest Tribble if necessary and find the amount of profit if you do round up.) | Step 1) Read the passage and find the information needed to set up the equations. Step 2) Set up the equation for the cost, C(x)= 1300 + 5x Step 3) Set up the revenue equation, R(x) = 15x Step 4) Set up the profit equation and solve it to find the profit. P(x) = 14x - (1300+5x) = 14x-1300-5x = 9x-1300 Step 5) Set the Profit equation equal to zero. 0 = 9x-1300 +1300 +1300 1300 = 9x --------------- 9x x= 144.44 Step 6) Round up and do BEP steps to find the amount of profit. P(145) = 9(145)-1300 P(145) = $5 | -- x-value represents time and the y-value represents amount -- cost = fixed cost + variable cost -- revenue = ____ x -- profit = R (x) - C(x) -- BEP - P(x) = 0 or R(x) = C (x) | how to evaluate word problems | the BEP and the steps I have to do if I round up | arely.escoto96@yahoo.com | ||||

47 | 7/1/2013 9:53:10 | Escutia | Leo | To solve a linear model word problem we must have records of two times and two amounts then we can have x be time and y be amount and now we have two "points". We can use the slope formula to find "m", Once we've done that then we need to plug in one of the points and the slope and solve for "b". Now we have our equation and we can use it to find the amount if we are given a time to plug in. | The word extrapolating means that we can assume that the pattern we are given will continue. For example if we have two points on a graph if we extrapolate, we can extend the lines further that just where the points land. | Erica enjoys making flower crowns in her spare time. During her first week of making them, she made 8 crowns. During week 9 she made 126 because she became more skilled and faster at making them. Assuming her productions follow a linear model, a) Write the linear equation to model production; b) Calculate how many crowns Erica made during week 5; c) Predict how many crowns she will have made by week 26, assuming this pattern continues | First we have to look at our two times and our two amounts, if we look at both we can create the points (1,9) and (9,126). Now we have to plug this into the slope formula, so; 129-9/9-1=120/8=15 m= 15 now we can plug in one of the points and the slope. 9=(1)(15)+b subtract 15 from both sides and we get b= -6, so the equation is y= 15x -6. Then we can find out how many she sold during week 5 by plugging in x (y= 15(5)- 6) and we get 75 - 6 which is 69. THis works the same way if we want to predict how many she'll make, (y= 15(26) -6) and we get 390 -6 which is 384. | The two types of costs that we have are fixed costs and variable cost. Our fixed costs are things that don't change dramatically, things such as rent or paying for utilities. Our Variable costs are those costs which vary from month to month, this could be what you decide to make as produce this month and how much of it you want. | The revenue we make is just the money we bring in, such as getting a paycheck at the end of the week, the number on the paycheck isn't really our profit because we have to look at our spendings. We have to take our income and subtract rent, utilities, food, gas and the money we have left over, if any, then that is our profit. | Erica was making too many flower crowns to keep for herself so she decided she could start a small business by selling them. It costs her $2600 for rent and utilities and $3 for the supplies that each crown needs. She sells each crown for $6. Write her a) Cost function b) Revenue function c) Profit function and d) Estimate the number of flower crowns she will need to sell in order for her to break even. | To find the cost function we have to take the fixed cost and add it to the variable cost, so it would be C(x)=2600 +3x. To find our revenue function we look at the price she sells her product at R(x)= 6x. The profit function is revenue -cost, so P(x)= 6x -(2600 +3x) = 6x -3x -2600 = 3x -2600. Then we make it equal to zero to find out how much she needs to break even. So it would be 3x -2600= 0 then 3x= 2600 and divide by 3 to get 866.66667 but we have to round up because we're using a part of a crown so we round it to 867, she needs to sell 867 to break even. | I need to remember that to find profit I need to think of PRICE. | I understood concept 6 very well and concept 7 was tricky at first, but i feel strongly about it now. | I undertand both of these concepts now. | leoescutia@yahoo.com | ||||

48 | 6/27/2013 15:47:38 | Estrada | Leslie | In order to solve a linear model word problem there are a series of steps that need to be done. To start off, you have to read the word problem carefully and highlight the key points. From the word problems you can set up two ordered pairs and keep in mind that the x-value always represents time and the y-value always represents the amount of something. When solving a word problem you also have to "extrapolate" which is just a fancy word for estimating the further value. Then once you know what the problem is asking for you can use the slope formula, y=mx+b, and f of x formula to solve for the linear equation. | Extrapolating means to basically estimate a Varible outside of what is given. For example if the pattern is 2,4,6,8,10,12 & you guess that the 10th term will be 20 you are basically extrapolating the next term. | Connie plays Volleyball throughout the week and likes to track her progress. Every week she has Volleyball Tournaments and she keeps track on how many serves she makes. During her 1st week she made 4 serves. Durning week 25 she made 144 serves. Assuming the pattern follows a linear model, a) write a linear equation to model her serves consistency; b) calculate how many serves Connie had made on the 6th week and; c) predict how many she will make on the 47th week if this pattern continues. | Well I circled the important a facts like the weeks and how many serves Connie made. Afterwards I used the slope formula which is y sub 2 minus y sub 1 over x sub 2 minus y sub 1. I found that 5 is our slope so I plug it in to y=mx+b and I get that b=19. Afterwards I do as the problems says & do the f of x to find how many serves she did on the 6th week and the 47th week. After pluging in y=5(6$+19 for the 6th week mark, I got 49 serves and for the 47th week I plugged in y=5(47)+19 and got 254 serves. | The two different types of cost that we have are Fixed Costs and Varible Cost. Fixed Cost is basically what you have to pay monthly such as rent, utilities, advertising, etc. Varible Cost is how much it cost to make each item. The difference between the Fixed Cost and the Varible Cost is te fact that the Fix Cost is consistent and basically the same amount all the time while Varible Cost all depends on how much you sell that day or how many items you decide to produced. A similarity that they both have is that they make up the revenue. | The difference between revenue and profit is that the profit is basically the income that the business gains and revenue is the amount of money you will put the item to sale including how much money it cost you to make it plus how many of them you made. For example the revenue would be the cost of the item while keeping in mind how much it cost you to make & how many you made. The profit for example is how much many you gain while already taken care of the money cost, for example: if you sell a ball at $20 but it cost you only $11 to make the profit of that ball is $9. | Connie is opening a volleyball business. If it cost Connie $2900 for monthly equipment and rental fees, and $4.75 for supplies for each volleyball. If she sells each volleyball for $26. Write a) Cost Function ; b) Revenue Functions; c) Profit Fumction; and d) estimate the number of volleyballs Connie will have to sell in order to break even( round up to the nearest decimal and find the amount of profit if you do have to round up). | The first step is to figure out the Cost Function , a) c(x)=$2900 + 4.75 Then we find the revenue, b) R(x)= $26 next is the profit, c) P(x) = 26x -(2900+4.75x) so you distribute the subtraction sign and you get 26x-2900-4.75x so we combine like terms and set it equal to 0 , P(x) 21.25x-2900=0 and you add 2900 to both side & divide by 21.25 and you will get a decimal so I rounded to 137 volleyballs. Then since we had to round we plug that number back to the equation and we get P(137)=11.25 | The most important facts that I need to remember are the formulas that are need to solve the problems and especially for the business problems though I'm sure with practice will be easy. | I understood concept 6 the most. I felt like it was pretty straightforward and it was something I already knew how to do. | I understand both concepts pretty well but I know that the one that will might cause me some trouble will be concept 7 because of all the vocabulary words & the various equation that will need to be memorized to do the problems. | leslie2926@yahoo.com | ||||

49 | 8/10/2013 15:57:45 | Estrada | Jeanette | To begin with, you take the time and amount and plug them into the ordered pairs time being the x-value and amount being the y-value. After that, use the slope formula to find the slope using the two ordered pairs. Then, plug in one of the ordered pairs with the slope into the slope intercept form of the equation (y=mx+b) to find the equation. Once you find the equation you can use it to plug in any time value to find the amount for that time value or vice versa. | The word extrapolate means to estimate the values beyond the known range. For example if we only know 2 points on the line we can extrapolate more points by extending the line to find points farther down the line. | Austin and his best friend Alex love making videos when they are bored so they decided to make a YouTube channel together. Their YouTube channel only got 25 channel views at the end of the first day. After 30 days, they already had a total of 344 channel views. Assuming their channel views follow a linear model, (a) write the linear equation to model the number of channel views they get every day; (b) calculate how many views they had after 14 days; and (c) predict how many total views Austin and Alex's YouTube channel will have had after 74 days assuming the same pattern will continue. | Given that Austin and Alex received 25 channel views the first day and 344 views after 30 days we can make these numbers the two ordered pairs we will use to find the slope [(1,25) and (30,344)]. To find the slope, use the slope formula which mean we will subtract 25 from 344 and 1 from 30 to get the fraction 319/29 which simplifies to 11, the slope of the line. After we have the slope we can plug it into the slope intercept equation along with one the the ordered pairs, (1,25). (25)=11(1)+b, after subtracting 11 from both sides, the answer for the y-intercept will be 14 making the linear equation y=11x+14, the answer to (a). For part (b) we have to calculate how many views Austin and Alex got after 14 days;in mathematical terms we have to find f(14) for the linear equation. For that we just plug in 14 in the x-value and after solving we would find it equal to 168. The answer to (b) would be 168 views. Finding the answer to (c) is similar to what we did in (b); we have to plug in 74 to the x-value of the equation and solve. The answer would turn out to be 828 meaning they got 828 channel views after 74 days. | In businesses we have two types of costs, fixed costs and variable costs. Fixed costs are costs the don't change because they may include utility and rent bills that remain the same;on the other hand, variable costs change every month because it is the cost of the items you sell so every month you sell a different amount and therefore you produce a different amount. | Revenue is how much you charge for every item you sell and profit is the difference between the price that you bought it for and the price that you sold it for or the money you make out of it. | Austin loves eating and making pizza so he opened up a pizza parlor. It costs $2,500 for monthly equipment and rental fees, and $7.40 for supplies. He sells each pizza for $11.25. Write his (a) Cost Function; (b) Revenue Function; (c) Profit Function; and (d) estimate the number of pizzas he will have to sell in order to break even (round up to the nearest pizza if necessary and find the amount of profit if you round up). | In this problem the fixed cost is $2,500, the variable cost is $7.40,and the revenue cost is $11.25. The Cost Function is the fixed cost + variable cost so in this case it would be c(x)=2,500+7.4x. The Revenue Function is just the revenue price so in this case it would be R(x)=11.25x. Finally the Profit Function is the revenue - the cost; in this case it would be P(x)=11.25x-(2,500+7.4x). The minus before the parenthesis distributes and after combining like terms you will end up with P(x)=3.85x-2,500 for the Profit Function. After that, equal the equation to zero and solve; you will get 649.35 but it will round up to 650 pizzas being the BEP (Break-Even-Point). To find the profit of the BEP plug the number into the Profit Function, 3.85(650)-2500. After solving you will be getting 2.5 or $2.50 as the small profit Austin makes from his new business. | cost, revenue, and profit | the business problem vocabulary | none | jeanjean101@icloud.com | ||||

50 | 8/18/2013 23:55:58 | Fernandez | Anthony | The first step to solving a linear model is to find the time frame of the first situation which will represent the x-value and then you find the amount of the subject that goes with it that will represent the y-value of the first ordered pair. The next step is to identify the second ordered pair of the problem by reading another time frame and amount number. Then by having both ordered pairs you must find the slope of the them by using the rise over run technique. You then put the slope in the slope intercept form and solve for b by plugging in any of the two ordered pair in the equation. Once you finish that process you have found the linear equation and just finished a part of the problem. The second must be solved by find the F(x) of the linear equation. So the next step is to plug in the number hat was given to solve for and evaluate the problem. Once you evaluate correctly you have solved the second part of the equation. To solve the last part you need extrapolate the asked time from of the equation in which you plug in for x and solve the problem to find the total amount. BY doing all of this you would have found out how to solve a linear model word problem. | The extrapolate means to predict the future amount of a linear model or just to predict something about the equation. An example would be the problem tells you to extrapolate the how many total of something would be in 52 weeks. This is asking us to predict the amount of the problem in 52 weeks to extrapolate is to predict. | Anthony has finally become a superhero and created his own armored suit that he was inspired from Iron Man after years of school, hard work, and major fundraising for the supplies. In his first week of being a superhero, he saved 50 lives from harms way. By the 5th week he saved about 250 lives. Assuming his hero work follow a linear model , A.) write the linear equation to the lives he has saved; B.) calculate how many lives he saved by the 10th week; and C.) predict how many total lives Anthony will have saved by the 22nd week assuming his heroic patterns continue. | The first step to do is to find the ordered pairs that are read as the time and the amount of something so in this case the first ordered pair is (1,50) since it says first week and 50 people and the second is (5,250) since it said 5th week and 250 people. Then you get the ordered pair and put it to rise over run equation and solve to find the slope. Once you found the slope which is 50 you plug it in a slope intercept form which is y=50x. Using the equation you hen solve for the 10th which is asked for so you plug in the 10 in the x spot, solve and then you get 500 lives. Lastly you plug in the asked number which is 22 and solve again and then at the end you should 1,100 lives. By doing all this we get all three answers that were asked for. | The two type of costs are fixed costs and variable costs. The both have in comparison is that they both take money out of the profit and affect the whole equation. The difference is that the cost are not both fixed in a sense that the fixed costs is the same every month like a rent or paying for utilities. Yet the variable costs is different every time and can be less or more at the end of the month like how much it cost to make a product. The varied cost can change whether you are making to make more or less but the fixed is the same no matter what happens to your business. | The difference revenue and profit is that revenue is the cost of the item that you sell while the profit is your total amount of money you made after paying all of your expenses. For example I am running a sand which shop in the city and the cost of one sandwich is 5 dollars that is my revenue. At the end of the month after I paid my fixed cost of utilities and my varied costs for ingredients I have a total of $50,000 left over and that is my profit. | Besides being a great super hero, Anthony runs a pizza shop in the heart of the city. It costs him $1400 for monthly equipment and rental fees, and $4 to make pizza. Anthony sells each pizza for $8. Write the (a) cost function; (b) revenue function; (c) profit function; and (d) estimate the number of pizzas Anthony will have to sell o break even ( round up if needed to be). | The first to solve the problem is to first find the varied cost and the fixed cost in the story. Once you find them you put them in the equation c(x)=1400+$4x you can find the revenue next and see that it is $8 dollars so the equation would r(x)=$8x. Next step is to find the profit function so first you must fill the equation P(x)=R(x)-C(x). So plug in the revenue and then plug in the numbers and distribute the negative and you should have your profit function. Lastly you need to find how much you need to break even so you must solve your equation of the profit function by setting it to zero. By doing this you find how much you need to break even so after following simple algebraic rules of solving equations you should get 350 pizzas needed to break even. By solving all these functions and solving for break even you have solved this Profit-Revenue-Cost word problem. | The most important facts I need to remember are the equation functions for the profit revenue problems. Also I need to remember the use of reading skills to identify the ordered pairs in linear model word problems. | The part that I understood the most is that linear model problems have to be read carefully and thoroughly to find the ordered to go with them and to know what the problems are asking you for. | The par I am still confused on is the profit problems because I get mixed up of which numbers to use and sometimes I forget to round and see what number is needed to break even in the problem. | tfernandez1612@yahoo.com | ||||

51 | 8/18/2013 23:56:02 | Fernandez | Anthony | The first step to solving a linear model is to find the time frame of the first situation which will represent the x-value and then you find the amount of the subject that goes with it that will represent the y-value of the first ordered pair. The next step is to identify the second ordered pair of the problem by reading another time frame and amount number. Then by having both ordered pairs you must find the slope of the them by using the rise over run technique. You then put the slope in the slope intercept form and solve for b by plugging in any of the two ordered pair in the equation. Once you finish that process you have found the linear equation and just finished a part of the problem. The second must be solved by find the F(x) of the linear equation. So the next step is to plug in the number hat was given to solve for and evaluate the problem. Once you evaluate correctly you have solved the second part of the equation. To solve the last part you need extrapolate the asked time from of the equation in which you plug in for x and solve the problem to find the total amount. BY doing all of this you would have found out how to solve a linear model word problem. | The extrapolate means to predict the future amount of a linear model or just to predict something about the equation. An example would be the problem tells you to extrapolate the how many total of something would be in 52 weeks. This is asking us to predict the amount of the problem in 52 weeks to extrapolate is to predict. | Anthony has finally become a superhero and created his own armored suit that he was inspired from Iron Man after years of school, hard work, and major fundraising for the supplies. In his first week of being a superhero, he saved 50 lives from harms way. By the 5th week he saved about 250 lives. Assuming his hero work follow a linear model , A.) write the linear equation to the lives he has saved; B.) calculate how many lives he saved by the 10th week; and C.) predict how many total lives Anthony will have saved by the 22nd week assuming his heroic patterns continue. | The first step to do is to find the ordered pairs that are read as the time and the amount of something so in this case the first ordered pair is (1,50) since it says first week and 50 people and the second is (5,250) since it said 5th week and 250 people. Then you get the ordered pair and put it to rise over run equation and solve to find the slope. Once you found the slope which is 50 you plug it in a slope intercept form which is y=50x. Using the equation you hen solve for the 10th which is asked for so you plug in the 10 in the x spot, solve and then you get 500 lives. Lastly you plug in the asked number which is 22 and solve again and then at the end you should 1,100 lives. By doing all this we get all three answers that were asked for. | The two type of costs are fixed costs and variable costs. The both have in comparison is that they both take money out of the profit and affect the whole equation. The difference is that the cost are not both fixed in a sense that the fixed costs is the same every month like a rent or paying for utilities. Yet the variable costs is different every time and can be less or more at the end of the month like how much it cost to make a product. The varied cost can change whether you are making to make more or less but the fixed is the same no matter what happens to your business. | The difference revenue and profit is that revenue is the cost of the item that you sell while the profit is your total amount of money you made after paying all of your expenses. For example I am running a sand which shop in the city and the cost of one sandwich is 5 dollars that is my revenue. At the end of the month after I paid my fixed cost of utilities and my varied costs for ingredients I have a total of $50,000 left over and that is my profit. | Besides being a great super hero, Anthony runs a pizza shop in the heart of the city. It costs him $1400 for monthly equipment and rental fees, and $4 to make pizza. Anthony sells each pizza for $8. Write the (a) cost function; (b) revenue function; (c) profit function; and (d) estimate the number of pizzas Anthony will have to sell o break even ( round up if needed to be). | The first to solve the problem is to first find the varied cost and the fixed cost in the story. Once you find them you put them in the equation c(x)=1400+$4x you can find the revenue next and see that it is $8 dollars so the equation would r(x)=$8x. Next step is to find the profit function so first you must fill the equation P(x)=R(x)-C(x). So plug in the revenue and then plug in the numbers and distribute the negative and you should have your profit function. Lastly you need to find how much you need to break even so you must solve your equation of the profit function by setting it to zero. By doing this you find how much you need to break even so after following simple algebraic rules of solving equations you should get 350 pizzas needed to break even. By solving all these functions and solving for break even you have solved this Profit-Revenue-Cost word problem. | The most important facts I need to remember are the equation functions for the profit revenue problems. Also I need to remember the use of reading skills to identify the ordered pairs in linear model word problems. | The part that I understood the most is that linear model problems have to be read carefully and thoroughly to find the ordered to go with them and to know what the problems are asking you for. | The par I am still confused on is the profit problems because I get mixed up of which numbers to use and sometimes I forget to round and see what number is needed to break even in the problem. | tfernandez1612@yahoo.com | ||||

52 | 6/27/2013 22:01:48 | Figueroa | Jessica | First u look for two pairs of a certain time and amount. then you put the numbers into the slope formula. once you get the slope you use one of the pairs plus the slope and put it into slope-intercept form and solve for b. once you have the equation you start to plug in other times into the x and get the amount for that time. | It means that since we assume that there is already a pattern we are going to go farther using the pattern. | Katherine want to open a organic lemonade company. During the 1st week she sold 7 cups of lemonade. during the 13th week she sold 67 cups of lemonade. assuming that her sales follow a linear model. a) write a linear equation to model the cups of lemonade sold. b) calculate how many were sold on the 5th week. c) predict how many will be sold on the 34th week. | First we get out pairs of coordinates (1,7) & (13,67). then we put it in the slope formula. our slope should come out as 5. then we get one of the two coordinates and the slope and plug it into the slope-intercept form, 7=5(1)+b. then you solve for b which should be -2. then you'll have your equation y=5x-2. then for the next question you get the other number of time which is 5 and plug it into the equation and solve for y. y=5(5)-2 and once you solve ur answer should be 23 cups of lemonade. then you solve for the last number of time which is 34. y=5(34)-2 and once you solved you should get 168 cups of lemonade. | First we have fixed cost which is a constant amount of money that you pay monthly. Then there is variable cost which differs from time to time because it is the amount you gain per item sold. Both of these are used to find the break even point in a business. | the revenue is the amount each item cost and the profit is the amount that you earn after everything has been paid off. for example if you own a popular restaurant the revenue would be the amount each meal cost in total but the profit will be what you get after you paid the workers, gas, electricity, and supplies. | Katherine is opening a organic lemonade company. it cost her 2500 for monthly equipment and rental fees, and $2 for supplies for the lemonade. She sells each organic lemonade for $4. write her (a) cost function; (b) revenue functions; (c) profit functions; and (d) estimate the number of organic lemonades she will have to sell in order to break even (round up to the nearest organic lemonade if necessary and find the amount of profit if you do round up.) | first we will get the cost function which is the fixed cost plus the variable cost, c(x)=2500+2x. then we will get the revenue function which is the total amount each item is sold for, 4x. then we will get the profit function which is the revenue function minus the cost function, 4x-(2250+2x). this isn't your final equation you have to simplify it to get the right equation, p(x)=2x-2250. lastly we will solve this equation and find the amount of organic lemonades that need to be sold which is, 1125 organic lemonades. then we plug in the amount that needs to be sold and see if we get a profit. p(1125)=2(1125)-2250. the answer ends up being zero because it is the BEP of the total which means you have to sell more then the amount needed to make a profit. | You need to remember the equations for the different problems.. | I understood the linear equations better even though i terrible at explaining steps at times. | I am a little shaky on concept 7 but i think with a bit more practice ill get the hang of it. | bluejessica54@yahoo.com | ||||

53 | 6/27/2013 23:26:50 | Figueroa | Esmeralda | When solving a linear word model it is important to find the ordered pairs using time (x-values) and amount (y-values) found in the text. With those ordered pairs, plug them into the formula: y2-y1/x2-x1 to find m. Plug m into slope intercept form to find b. Then, put everything together in an equation. In these particular word problems, there are additional questions asking "how much was made at this time" and "if the pattern continues, how much will there be at this time". Using f(x), plug in the given time to the equation. | Extrapolating basically means to predict what will happen next, how much there will be. In these word problems, extrapolating is needed to solve problem c), which asks "if the pattern continues...". Graphs can also show that: the original ordered pairs we come up with at the beginning are plotted on a graph. When a line is drawn between them, that line could extend further and give an idea of what comes next, in other words, predicting the future. | Noemi loves to bake and has decided to sell her mini confectionery creations. That first week, she sold 55 mini creations altogether. Thanks to the help of friends, family, advertising and Facebook, by week 6, she sold a total of 450 of her confectioneries. Assuming her sales follow a linear pattern, (a) write the linear equation to model her sales; (b) calculate how many mini creations she sold by week 4; and (c) predict how many she will have sell by week 12 if this pattern continues. | (a) First, find the ordered pairs by looking back at the word problem: (1, 55), and (6, 450). Plug them into y2-y1/x2-x1: 450-55/6-5 = 395/5 = 79 = m. Once m is found, plug it into slope intercept form to find b: 56 = (79)(1) +b. (-23) = b. Plug them once again into slope intercept form to form the linear model equation: f(x) = 79 x - 23. (b) To find how much has been sold during week 4, plug 4 into x: f(4) = (79) (4) -23. This amounts to 293 confectioneries. (c) To extrapolate how much will be sold during week 12 if the pattern continues, do the exact same thing as problem (b): f(12) = (79) (12) -23. The end result is 925 confectioneries. | Two different types of costs that there is are fixed cost and variable cost. Fixed costs are always paid monthly, and remain stable every month. Fixed costs are used for rent, utility bills, advertising, etc. Variable costs are different from fixed costs in that it is mostly dependent on how much money is spent towards making something. Fixed cost is remains the same all the time whereas variable cost varies because the same amount of stuff is not made at the same amount of time and neither is the same amount of stuff sold at the same amount of time. | Revenue is basically how much an item is put for sale while profit is what is left over for the entrepreneur by subtracting the costs from the revenues. This is mostly used for business purposes. | Noemi is starting her own bakery of mini confectionery creations. It costs her $2750 for monthly equipment and rental fees, and $.80 to bake each mini creation. She decides to sell each of her mini creations, no matter what it is, for $4. Write her (a) cost function; (b) revenue function; (c) profit function; and (d) estimate the number of mini confectionery creations Noemi will have to sell in order to break even (round up to the nearest mini creation if necessary and tell how much profit she will make if she has to round up.) | (a) The cost function is made up of the fixed cost ($2750) and the variable cost ($.80) and is formatted into the function: C(x) = 2750 + .8x. (b) The revenue function is basically just how much each mini creation costs, which is $4, so the function would be: R(x) = 4x. (c) The profit function is found by putting all the variables together: P(x) = 4x - (2750 + .8x). The negative sign is used to distribute to the parentheses: P(x) = 4x -2750 -.8x. Combine like terms: P(x) = 3.2x -2750. This is the profit function. (d) The profit function is used to estimate the number of mini creations Noemi will have to sell in order to break even: 3.2x -2750 = 0. Add 2750 to both sides, divide by 3.2, and the end result is 859.375. Because there can't be a decimal as the answer ( it is not possible to sell a decimal amount of something), it is important to round up to 860 mini creations. To find how much profit she will make out of selling 860 mini creations, we plug 860 into the equation: P(860) = 3.2 (860) -2750. This equals $2 profit that she will make. | Extrapolating (predicting), the phrase: "follows a linear model", cost (fixed and variable), revenue, profit, and BEP (break even point). | Plugging in the appropriate information for linear models, especially because it used slope intercept form and wasn't too specific on the details. | I found the cost, revenue, profit problems a bit more challenging because it involved money and was extremely specific on the details of the business and the finances and stuff. | figueroa.esme@gmail.com | ||||

54 | 6/22/2013 22:47:58 | Filsinger | Stephanie | The first step in solving a linear model word problem is to take information that relates to each other and can be put into ordered pairs. For example, if the word problem says there were 4 butterflies in the first week and 16 butterflies in the third week, we would set up two sets of parenthesis. The x value will be our time and y value will be the amount of things. So it would look something like this (1,4) (3,16). Once we have these two points, we solve for slope using y2-y1/x2-x1. From there we put it into y=mx+b form. Then we plug in a point to solve for b. once we have b we put it back into slope intercept form. This is the linear equation. Once we have this linear equation ( assuming that the butterflies always increase in the same rate) we can predict how many butterflies will be there in any given week by plugging that number in as x. | Extrapolating means that we take the information that we already have and predict what will happen if we continue following the same linear model. This means if we have a part of a graph, we can extend the line with the same linear model to find out what would happen way at point ex. (41,50) or somthing that is farther out than our original segement. | James P. Sullivan designs and sells monster costumes. In his first week of business, he sold 4 costumes. Word got around, and by his fifth week, he hd sold 32 costumes. Assuming his sales follow a linear model, (a) write the linear equation to show his costume sales, (b) calculate how many costumes he had sold in week 2, and (c) calculate how many costumes he would have sold by week ten of his business if his pattern continues. | The first thing we would do in solving this linear model is look for the info to go into the ordered pairs. For each set of parenthesis, we will put the number of weeks as our x ( because it is our time measurement) and will put the amount of costumes as our y value. So they would look like this (1,4) and (5,32). Then solve for slope using y2-y1/x2-x1. Our answer should be 7. Form there we set up y=mx+b. when we do this, we should also plug in a point. (Do the one with the easier number to work with =D) so it could look like 4=(7)(1)+B. so four equals seven plus B. subtract seven from both sides and you get B=-3. You final linear model equation is y=7x-3. So now we can calculate how many costumes he had sold by plugging that number of week in as your x value. So in week two, we would say y=(7)(2)-3. And y= 11. For finding how many he will sell by week ten, we do the same thing. Y=(7)(10)-3. And y=67. | The two different types of costs that we have are fixed and variable. Fixed costs are costs that you have to make every month and they pretty much stay the same from month to month. These would be things such as rent, utilities, amd advertising. Variable costs are costs that vary depending on how much of something you produce that month. So if it cost 25 cents to make every pencil, we have to multiply .25 by however many we made that month. When we add these together is when we get our total cost. | Revenue is the amount of money you earn from each product that you sell. This is not all of your "take home" money though because you still have to pay for your supplies. What you get to keep after you subtract out what you had to spend on the business is your profit. For example, class of 2015 decided to sell t shirts. Each t shirt costs 2 dollars to make. The class is selling each shirt for 7 dollars each. Once you take your revenue (7) and subtract out your cost(2) the class gets a profit of 5 dollars off every shirt. | James P. Sullivan is continuing to sell his costumes. It costs him $2000 for monthly equipment and rental fees, and $10 for each monster costume. He sells each costume for $40. Find his (a) cost function, (b) revenue function, (c) profit function, and (d) estimate how many costumes he will have to sell to break even. (Round up to the nearest costume if necessary and find the amount of his profit if you do round up. | The first thing it says to find is the cost function. Tomdo this, we add our fixed cost and variable costs. That would be 2000+ 10x. X represents that number of costumes. Our revenue function is the amount we getmoff of each costume so it is 40x. To find our profit function, we subtract the cost from the revenue. That would be 40x-(2000+10x). Distribute the negative. . So 40x-2000-10x= 30x-2000. 30x-2000 is our profit function. To find our bep, we just solve for x. Move 2000 to the other side of the eqaul sign and we get 30x=2000. Divide both by 30 and x eqauls 66.7. Because it is impossible to sell.7 of a costume, we must round up. So he has to sell 67. Costumes. Then, we must find the small amount of profit that he makes. To do this, we plug 67 in as x in our profit function. (30)(67)-2000= 10. So he made a profit of ten dollars. | I need to remember to always round up if the bep has even a .1 after it, even though that isnt logical to round up. | I feel like i pretty well understand both of these concepts. | I dont think im confused on either of these concepts. | Stephaf27@gmail.com | ||||

55 | 8/19/2013 11:37:27 | Flores | Valeria | Reading the word problem you can extract two sets of ordered pair. You will then solve for the slope using the formula y2-y1/X2-x1. You will then plug the slope into the equation y=mx+b as well as plugging in one of the ordered pairs and then sloving for b. | From the video, i pretty much thought that extrapolate means to predict how the line will go the line assuming that it follows a linear model. | Susie loves to read all kinds of books. During the first week o school she had read 5 books by the 13 week she had read 89 books. Assuming that her reads continue to follow a linear model(a) write a linear equation(b)calculate how many book she read by week 6(c) and predict how many book she will read by week 21. | The first thing i would do is find my ordered pairs which are (1,5) and (13,89). Then, i would solve the slope using y2-y1/x2-x1 which would end up being 7. so then i would plug in one of the ordered pairs and the the slope and solve for b. The answer would be -2 so the full equation would be (a) y=7x-2. for the next two all you do is change y to f(x) and plug in the week you would like to know how many books she read. (b)40 (c)145 | The two cost are Fixed cost and Variable cost. Fixed cost are things like monthly rent,water, electricity, gas and pretty much things which the price does not really change. Variable cost would be things like how many of each item you are making. It will not be the same every month and price varies. | revenue is how much youre selling the item for while profit is the extra money you receive from the revenue price. For example i bought a shirt for 2 dollars, i made adjustments and im raising the price to 7 dollars so my revenue would 7$. If i sell the shirt i have a profit of 5$. | Susie has so many books she is now starting up a book store business . It cost 4800 for monthly rent electricity and gas and 8 dollars for books supplies. She sells each book for 16. Write a Cost Function. Revenue Function, Profit Function, and estimate the number of book she must sell to break even. | The cost of tis problem would be 4800 as fixed and 8 as variable cost. A. C(x)=4800+8x Revenue would be !6$ so B. R(x)= 16$ to find the profit of you subtract 8 from 16 which would be 8 C. p(x)=8x-4800 to find the break even point just solve for x. so you add 4800 to both sides and divide by 8. D. the break even point would be 600 books. | what the break even point is, and the difference between revenue and profit. | i understood ALL of it. pretty easy concepts. | N/A | flores.vale96@yahoo.com | ||||

56 | 6/25/2013 20:25:32 | Franco | Laura | While solving a linear model word problem, it is important to set up two sets of ordered pairs. This ordered pair would be represented as (x,y) where x-value represents time and the y-value represents the amount. After you have figured out the two sets of ordered pairs, in order to find out the linear equation, you would have to find the slope and the 'b'. To find the slope, you would use the (y2-y1)/(x2-x1) formula. After you find the 'm', you would plug in one of the ordered pairs into the equation y=mx+b to find 'b'. After finding the linear equation, in order to find out an amount for future weeks to come, you would plug that into the x, which represents time and your outcome would be the y, the amount. | Extrapolating means to estimate the amount of an extension. For instance, if a problem asks you to predict how many books are sold in 18 weeks when it is only week 6, you will have to extrapolate the line on the graph and, using the linear equation, can predict how many books will be sold by then, assuming that the pattern continues. | Cindy loves baking cakes. She had recently opened a small cake shop in her little town. The first week, only 9 cake orders had been made. By week 5, 25 cake orders had been made. Everyone in that town knew she was just paying people to buy her cakes in order to look more popular than her rival, Gloria, who owned a small cupcake shop. Assuming Cindy keeps paying people to buy her cakes and it follows a linear model, (a) write the linear equation to model her orders; (b) calculate how many orders were made during week 3; and (c) predict how many orders will be made during week 28 if this pattern continues. | The ordered pairs to the word problem would be (1,9) and (5,25). Using the (y2-y1)/(x2-x1) formula, we will find out what the slope is. 25-9/5-1=4. The 'm' to the equation is 4. After this step you will use one of the ordered pairs to find out the 'b'. 9=4(1)+b where b=5. (a) The linear equation to this problem is y=4x+5. Using the linear equation, we will figure out how many orders were made during week 3. We know it has to be between 9 and 25. You will plug in the 3 into the x. y=4(3)+5 where y=17 (b) During week 3, 17 cake orders were made. Again, using the linear equation, we will predict how many cake orders will be made during week 28. 28 will be plugged into the x. y=4(28)+5 where y=117 (c) During week 28, 117 cake orders were made. | The two different type of costs include fixed costs and variable costs. The fixed costs include anything that is paid monthly and usually stays the same every month. For example, rent, utilities, and advertising would fall under fixed costs. However, variable cost is how much is costs to make an item. This cost usually varies and is based on how many items you decide to produce. | Revenue is how much you charge for each item sold. The profit is the revenue minus the cost. The profit is the actual money the business is making. Without this, the company could go out of business. For example, if Starbucks charges $5 for every coffee (revenue) and only spends $2 making every coffee, their profit would be $3 for every coffee sold. | Cindy started her own baking business. It costs her $1500 for monthly equipment and rental fees, and $3 for supplies for each cake made. She sells each cake for $10. Write your (a) Cost Function; (b) Revenue Function; (c) Profit Function; and (d) estimate the number of cakes Cindy will have to sell in order to break even (round up to the nearest cake if necessary and tell how much profit you will make if you have to round up). | Cost functions would be C(x)=1500+2x Revenue Function would be R(x)=10x Profit function would be P(x)= 8x-1500 The break even point (BEP)=8x-1500=0 8x=1500 x=187.5 rounded to 188 cakes P(188)=8(188)-1500 P(188)=$4 profit | remembering to tell how much profit is made if an item is rounded up. | writing the linear models and solving for the cost, revenue, and profit problems/ | remembering what goes where in the cost. profit, and revenue problems | lcdm41@gmail.com | ||||

57 | 7/31/2013 23:15:20 | Galaviz | Saul | Extrapolate the points you have found in the word problem, then use the formula m=y2-y1/x2-x1 to find m. Next you have to find certain weeks sales by using the equation f(x)=mx+b and like this, you can find any weeks sales. (sales used as an example) | The most important terms I need to remember are extrapolate, which is to plot two points, connect them, and find some information on whats in between. Like in a linear model, if you need to find whats in between or what continues on, you can use this to help you find what points you need. | Oliver loves playing Pokemon games all the time. Hes been a huge fan since the Pokemon game series started with Pokemon Red and Blue came out. Now he's partnered up with Game Freak and what not to make the the next generation Pokemon, the 11th generation; Pokemon Tan and Pokemon Olive. For the first week of their release, both games together sold 14 copies. By the sixteenth week, both games have sold a total of approximately 85 copies, he's happy now. Assuming Oliver's sales follow a linear model, (a) write a linear equation to model his sales; (b) calculate how many Pokemon USB Oliver and Game Freak have sold during week 8; and (c) predict how many Pokemon USB they sell during week 68, assuming this pattern continues. | You have to extrapolate first the week sales which will be: (1,14),(16.85). Then you start (a) which is to find the linear model, use m=y2-y1/x2-x1 which when you plot in the numbers, get m=85-14/16-1 getting 71/15=4.73=m. You then use the formula y=mx+b, plotting in m, x and y from a point, (14)=(4.73)(1)+b and solve it. 14=4.73+b, subtract 4.73 from each side. 9.27=b is your b. Then we continue (b) we use f(x)=mx+b to find the answer, plot in the variable, f(8)=4.73(8)+9.27, which gets you: f(8)=37.84+9.27 = 47.11 = your week 8 sales (f(8)). Then we need (c) f(x)=mx+b, plot in the variable, f(68)=4.73(68)+9.27, solving it, get f(68)=321.64+9.27= 330.91= your week 68 sales (f(68)). | We have fixed costs and variable costs, the difference between these two are that fixed costs are a monthly pay, such as utilities and electricity costs, and variable costs are how much it costs to make the product you're producing. | The difference between revenue and profit is that revenue is how much you charge the items your selling, while profit is how much extra money you have leftover after your costs. An example would be Oliver selling his USB video games for 8 dollars, and when someone buys them he makes 2 dollars in profit because after he's payed his costs, he still has that extra money leftover resulting in profit. | You are starting a new card game series to pay off your debt in Detroit. It costs you $250 for living with your mother as well as the food, and $3.50 for paper and sharpies to draw the cards. You sell each deck of cards for $11.50. Write your (a) Cost Function; (b) Revenue Function; (c) Profit Function; and (d) estimate the number of decks you will need to sell in order to break even (round up to the nearest deck if necessary and find the amount of profit if you do round up.) | First you need to find (a) the Cost function, which is C(x)=Fixed Costs+Variable Costs, plotting in the numbers, get C(x)=250+3.50x as your answer. For (b) you have to use R(x)=how much you sell each item(x), plugging that in, get R(x)=11.50x as that answer. Next for (c) you have to use P(x)=R(x)-C(x), plugging that in, get P(x)= 11.50x - (250+3.50x), then solving it, get to R(x)=8x-250 as your profit. Finally for (d) you need to check if you sales actually break even, so from (c), we have R(x)=8x-250=0, the add 250 to each side: 8x=250, divide 8 to each side, and get x= 31.25 decks, but it can't be like that because you have to round up to the nearest deck, and get x=32 decks. | The most important tip i need to remember is PRiCe, because it will help me remember how to find profit, because using it, P(profit) = R(revenue) - C(fixed cost + variable costs), helps me find it. | I understood the most from these two concepts was how to find f(x), because all you do is evaluate it in an equation. | These two concepts were very easy, no trouble whatsoever. | nostramagear@gmail.com | ||||

58 | 6/28/2013 21:11:14 | Gallardo | Miguel | okay so you have too look for time (x) and the rate of change (y). For example, they give you the information for week 1 only 3 books were sold and week 13, 87 books were sold. so you get the slope formula out of the ordered pair which would be (1,3) and (13, 87). you get the slope of 7. so you get a point and plug it all in y=mx+b and end with B=-4. then you get rewrite the equation with the corresponding numbers which would be f(x)=7x-4. And your basically done. | it is when we plot two given points which create a line. When thy ask us to predict in a linear word problem they are basically extending the line to figure out whats happening at the end of the line. | Jack loves to sell pumpkins as a hobby to local people. On his first week , he was able to sell 3 pumpkins and by week 13 he was able to sell 87. Find and use a linear equation, calculate how many pumpkins he sold during week 7 and predict how many he will sell during week 32. | well first you get the ordered pair from the equation which is (1,3) and (13, 87). Then you find the slope formula and get 7. You plug it into y=mx+b form by choosing a point. So i chose the smaller one and end with 3= 7(1)+b. you then you solve and get b= -4 and rewrite it in y=mx+b and end with f(x)= 7x-4. Then you do the rest of the problems and get the answers by plugging in the given weeks. | The two type of cost we have are fixed costs and variable costs. Fixed costs are paid monthly and stays the same price every month. An example of this would be rent, electricity and gas bills. A Variable cost is how much it cost to make the item. The cost varies because it depends on how much item you wish to produce that month. | The revenus would come from the price the business charges for a certain item. Profit is when you equal the amount of money you used and passes its BEP in order to make money. Revenus in real life is when the price tags say the money for the item and the cashiers charge it with tax. Profit would be like when a company is started with a certain amount of money and later is abke to far surpass it and make its company expand and become bigger. | Jack is starting a pumpkin business. It cost him $1500 for monthly equipment and $3.25 for supplies to grow each pumpkin. You sell each pumpkin for $14. Find the (a) cost function ; (b) revenus function; (c) profit function and (d) estimate the number of headphones you need to sell to break even. | You look for the cost function which formats into C(x)= fixed cost + variable costs. so it should end up looking like this: C(x)=1500+3.25x. then you find the revenue function which is the price charged for the item: P(x)= 14x. Then what i do is get the same equation and them subtract the first one. (Put the first equation in paratheses.) So you should get: 14x-(1500-3.25x). You distribute and combine like terms and end up with P(x)=10.75x-1500 which is your actual cost function. To fine the BEP, you have to set it equal to zero, add 1500 to both sides and divide by 10.75. you will end up with 140 pair of earphones. Then to find the profit available you plug in 140 to the cost function. and end up with 5 dollars profit to grow more pumpkins. :) | is the word PRICE since it will help creating the equations. Also the word Break Even Point. And the word extrapolate since it helps undersand linear models | Was the solving for cost, profit and revenu problems since i like money :) | It wasn't really confusing, just lengthy with all the reading. | miguel_gallardo3000@yahoo.com | ||||

59 | 6/25/2013 23:27:34 | Garcia | Ana | To solve a linear model word problem you take the number of the first week and the amount of what was sold on the first week into an ordered pair such as, (1,6) and then the number ff the last week and the amount of what was sold into another ordered pair such as (6,46) After, you plug the x and y values into y2-y1 over x2-x1 to get your slope. Then plug your slope and an ordered pair into y=mx+b and what ever is asked that is sold on a number of certain weeks you plug in the number of that week into the equation with your new slope and y intercept and solve to see how much. | Extrapolating means to know beyond of what is given to you. For example in a linear model word problem you need to extrapolate, meaning find out what is being sold of the weeks ahead by the few certain information they give you. | Ricky and Ana eat Pizza Hut every week because they have coupons for free bread sticks when they order a large pizza. On the first week they ate 12 slices of pizza and by the 4th week they had eaten 48 slices of pizza. Assuming there stomachs follow a linear model (a) write a linear equation to calculate how many slices they eat (b) calculate how many slices of pizza they had eaten by the 6th week (c) and predict how many slices they will have eaten by the 10th week. | First you need to make two ordered pairs. One of the first week and how many slices of pizza were eaten on the first week , which looks like this (1,12 )and the other pair of the last week and how many slices were eaten on that week. which looks like this (4,48). Then you plug both of the ordered pairs into y2-y1/x2-x1 to get your slope which will be 36/3 and then simplified into 12. Then you will use one of your ordered pairs along with your slope and plug it into y=mx=b to solve your b which will be 0. Then create a slope intercept equation using the new slope and b which is y= 12x. the to find how many slices of pizzas Ricky and Ana have eaten by the 6th week plug in 6 into the equation so you will solve 12(6) and get 72 meaning ricky and ana will have eaten 72 slices of pizza by the 6th week. To predict how many slices of pizzas the two will eat on the 10th week simply plug in 10 into the equation and solve 12(10) which will then mean that Ricky and Ana will have eaten 120 slices of pizza by the 10th week because of Ricky's big stomach. | The two different types of costs are fixed costs and variable costs. A fixed cost is the amount of money that is required to be payed monthly, for example: electricity, advertising, rent. A variable cost is how much it is to make each item, this varies on how much items are produced each month. | Revenue is how much you charge for each item that you sell and the profit is what you make out of your revenues and your costs subtracted. For example, i charge a dollar for a caramel apple but it takes me o.75$ to make each and every one. The profit i will be making is 0.25$ for each apple. | Ricky and Ana sell caramel apples to make some money so that they can eat out at a nice restaurant the day of their monthly anniversaries. It costs them 25$ dollars for monthly equipment and 0.50$ for each apple. They sell each apple for 1$. (a) Write the cost function, (b) revenue function (c) profit function and (d) estimate the number of apples they must sell in order to break even (round up the nearest apple if necessary and find the amount of profit the two round up). | First you must find the cost function which is the fixed cost plus the variable cost. So the cost function will be: c(x)= 25+ 0.50x Then find the revenue cost which is how much each caramel apple Ana and Ricky sell it for so the revenue function will be: r(x)= 1x Then it asks for the profit function which is the revenue minus the cost function which is (1x)-(25+0.25x), make sure you distribute the negative so that your get 1x-25-0.25x and after subtract the two like terms 1x-0.25x to get your total profit function of: p(x) 25x- 0.75. Then to get the break even point add a zero to the end of the profit function which will be 25+0.75=0 and subtract 0.75 to each side and you will then get 25= 0.75 and have to divide 25 on each side and will get the answer of 33.3 but since you must add to the nearest tenth it will be 34 caramel apples that Ricky and Ana have to sell in order to make some money to go on their dinner date. | what a Break Even Point, cost, revenue, and profit function are and how to solve business problems. linear model word problems is also something else i need to know how to solve. An important thing about them is to know the ordered pairs. | solving for linear model word problems. | solving for business problems. | garciaaaa13@yahoo.com | ||||

60 | 6/28/2013 18:46:53 | Garcia | Louis | The first step is that you have to see the information it gives you on what week what sold how many. After you get the ordered pair you have to use the slope formula to find the slope. After, you use the slope- intercept form equation and plug in one ordered pair and find b. Then you have the equation and it asks you for a certain week and you plug that in into x and then you get your answer. | Extrapolating means to continue a pattern even though it has stopped at a certain point estimating that the line continues to be constant. For example. if there is a line from points (1,2) to (4,7), it means to continue the line even though the last know point is (4,7). | Xavier always wanted to buy new things but couldn't because he didn't have enough money. He decided to start selling his collection of toy cars, in the first week, he sold 5 cars. By the eighth week he sold 33 cars. Assuming his sales follow a linear model, (a) write the linear equation to model his sales; (b) calculate how many cars he would've sold in 6 weeks; and (c) predict how many toy cars he will sell in 15 weeks if this pattern continues. | So i read the equation and i see that in the first week he sold 5 cars and in week eight he sold 33 cars. So it gives me the ordered pairs of (1,5) and (8,33). I plug it in into the slope formula and get m=4. then i plug in a ordered pair of Ill choose (1,5) and get the slope intercept form which is f(x)=4x+1. That is the linear model equation, now i plug in for x both 6 for week 6 and 15 for week 15. For week six he sold 25 cars and in 15 weeks he will sell 61 toy cars. | The two different type of costs are fixed and variable costs. Fixed costs is things that have to be paid monthly and the amount owed stays the same. Variable costs are for the things you are selling in how much it cost to make what you are selling. | The difference between revenue and profit is that revenue is how much money was brought in from sales. Profit is earning more than what the cost were for the things needed. For example, if i spend 30 dollars on lemonade juice and i make 40 dollars selling cups of juice. The revenue is 40 dollars but the profit is 10 dollars because it was more than what i paid for. | Xavier started a toy car selling company. It cost him $1000 for monthly equipment and rental fees, and $.50 for supplies for each toy car. He seals each toy car for $1.25. Write your (a) cost function (b) Revenue function (c) profit function; and (d) estimate the number of toy cars he will have to sell in order to break even(round up to the nearest toy car if necessary and find the amount of profit if you do round up). | First i look at the fixed and variable costs. I see that the fixed cost is $1000 and the variable cost is $.50. I put in the equation for cost and it goes like this a) c(x)= 1000+.50x. Then I find the revenue which is $1.25 and write the equation for revenue which is r(x)=1.25x. I finally put it togther in the profit equation p(x)=1.25x-(1000+.50x). After you simplify its p(x)= .75x- 1000. you put zero for x and add 1000 to both sides then divide by .75 and get that you have to sell 1,333.33 cars. You round up to 1,334 and plug it into the profit equation and get that you make a $.50 profit. | to remeber the equations for cost, revenue, profit, and break-even point (BEP). In the linear models, x is time and y is amount. | Writing linear models and evaluating for word problems. | trying to place the correct numbers in a business problem for the equations. | louisgarcia23@yahoo.com | ||||

61 | 7/23/2013 12:27:23 | Garcia | Adriana | A linear model consists of time and amout. X representing time and Y representin amout. If we assume the sales/amount will extrapolate or continue, then we can use the slope formula to figure out the slope. After we have that figured out, we use the slope intercept form. After that is figured out, we can plug any number representing time into X to figure out the amount. | Extrapolating assumes what the sales/amount will be after a certain amout of time. For example, if I read 2 books in 1 week, and 4 books the 2nd week, youre most likely going to assume i read a total of 6 books the 3rd week...or 12 books the 6th week. | Drake sells mixtapes/CD albums because he loves making music. He is slowly getting out there though. During his 1st week, his mixtape "comeback season" sold 15 copies. By the 6th week, he sold 95 copies. Assuming his sales follow a linear model, a) write the linear equation to model his sales, b) calculate how many sales Drake sold during the 4th week, and c) predict how many copies he will sell during week 19 if the pattern continues. | The first week, Drake sold 15 copies and the sixth week he sold 95. So X=time, Y=amount. (1,15) & (6,95). Now we plug that in the slope formula. So its (95-15)/(6-1) which equals 80/5 and that reduces to 16. Then we plug 16 into y=mx+b as M. im going to use (1,15) since its a smaller number than (6,95). so 15=16(1)+b. we subtract a6 on each side to get b alone and we end up with -1. So our new line is y=16x-1. now we can substitue any time for x and solve. so his 4th week Drake sold 63 copies because f(4)=16(4)-1 = 63. His 19th week, he will sell 303 copies because f(19)=16(19)-1 = 303. | There are fixed costs and variable costs. Fixed cost is paid monthly and stays the same, for example rental fees and monthly equiptment. Variable cost is how much it takes to make each item, it varies on how many items you decide to make. They are both costs but different kinds. | There is a pretty big difference betweem revenue and profit. Revenue is how much you charge each item that is sold and profit is revenue - costs, so what youre left with. For example, if i make head bands and it costs me 2 dollars to make 1, and i sell them for 5 dollars, i am making 3 dollars worth of profit. | Drake is finally getting a producer to help put together his music. It costs Drake 100 dollars every month to pay off his producer and 3 dollars for supplies to make the mixtape/CD. He sells each CD for 7 dollars. Write the a) cost function, b) revenue function, c) profit function and d) estimate the number of CDS he has to sell in order to break even. | To start off, we figure out the costs, both fixed and variable. Our fixed cost is $100 and out variable cost is $3. Our cost function is going to be our fixed cost plus our variable cost times x. So out variable cost is c(x)=100+3x. Next, our revenue is the amount we sell the item for times x, so our revenue function is r(x)=7x. Next, our profit function is the revenue function - the cost function which is p(x)=7x-(100+3x). We have to distribute the negative so it ends up being p(x)=7x-100-3 and once we combine like terms we have p(x)=4x-100. in order to solve the break even point, we set the profit function set to 0. So it looks like this 4x-100=0. we solve through and end off with 20. So Drake has to sell 20 mixtapes just to break even. | The most improtant facts, terms and tips i need to remember from these concepts are the buisness problems vocabulary words, and the word "price" to help me remember how to solve through. | The part i understood the most from these two concepts is the writing a linear models and evaluating for word problems, i had no trouble with that concept. | I am still a little confused about concept 7, writing and solving cost, profit and revenue word problems but ill understand with a little more review. | adriegarcia@rocketmail.com | ||||

62 | 7/25/2013 18:00:42 | Garcia | Susie | To solve a linear model word problem, you first find the key numbers that are followed by key words. So if it says one week the x will represent the number of week and the y value will represent the amount of what is to be found. Once the two points from the word problem are found we use the slope formula of y2-y1/x2-x1 and use the slope to plug into the slope intercept formula to find b. once you find b, you plug in the slope along with the intercept form to find how many objects were sold in the amount of weeks we are looking for. | In these word problems we need to make sure we extrapolate by extending the line to the other end of the graph. This makes us inter or predict that the line will be like further on. | Hannah loves her theater plays so much she wants to become a broadway star. She enjoys attending local plays to explore ways she can become a better performer. The first week of her senior year of high school she attends 6 shows. During her 10th week of senior year she had attended 24shows. Assuming her attendance to shows follows a linear model, (a) write the linear equation to model the number of shows she attended; (b) calculate how many shows she attended by Week 4. (c) predict how many total shows Hannah would have gone to by week 28 | First we find the slope by subtracting y2-y1 and deciding by x2-x1. And we get 2 as the slope. We plug in one ordered pair and the slope into the intercept formula. Once we plug it in we have 6=2(1)+b. subtract 2 on both sides and you get 4 as the y intercept. You then set the found slope (2) and found intercept (4) to f(x) and the linear equation is y=2x+4. We plug in 4 to find how many shows she had gone to by week 4 and we get 12. And for (c) we plug in 28 and have 2(28)+4 and equals 60 | The two different costs are the save because they both will involve in your business staying with enough money by giving you a place to make your actual products. The difference of the a fixed cost and a variable cost is that a fixed cost is always constant every month and you know that you need to pay that amount while a variable cost is not always constant due to not knowing how much you sell. So this results into the variables changing along with the costs. | A revenue is how much you will get depending on how much you sell each item without any other costs, while the profit includes all the cost that will be taken out and how much will be left for you to spend freely. | Hannah is selling some tickets for her next drama performance. It costs her $1500 for monthly equipment and rental fees, and $2 to print tickets. She sells each ticket at $5. Write (a) cost function; (b) revenue function; (c) profit function; and (d) estimate the number of tickets that is needed to sell to break even. | (a) is found in the equation 1500+2x. (b) is 5x which is the revenue (c) is 5x-(1500+2x) and turns into 5x-1500-2x once the negative is distributed (D) add 1500 to both sides then equal it to zero. Divide 3 on both sides and it equals 500 tickets | Extrapolate and making sure that the correct numbers are plugged into the correct equations. | Is understanding what the x and y values stand for in the ordered pairs of linear models. | I sometimes get confused on telling the difference of f,r, and v in solving cost, profit and revenue word problems. I have to double check my work and make sure that I plug in the correct numbers. | Sgarcia0596@gmail.com | ||||

63 | 6/27/2013 15:18:28 | Garibay | Kenia | 1. identify what the x-values are which deal with time 2. Identify what the y-values are which deal with an amount 3. Use the values and plug it into the (y2-y1)/(x2-x1) to get the slope (m) of the linear equation 4. plug in a coordinate from the problem (x,y) into the y=mx+b in addition to the slope found in step 3 5. Solve and you will have b which is the y- intercept of the linear equation 6. Plug in the slope and y-intercept found earlier into the y= mx+b in order to have the formula 7. Plug in any other values into the x to find what the person would have in x weeks if asked in the problem | Extrapolating means to extend the data to a future time in the linear equation. In other words to figure out what an amount would be at a time that continues if it were to follow the linear equation. | Andrew VanWyngarden started collecting record albums from thrift stores on the weekends. The first week, Andrew found 4 amazing records. During the fifth weekend, his collection consisted of 28 records. Assuming that Andrew record purchases followed a linear model, (a) Write the linear equation to model his records collection; (b) calculate how many records Andrew had during the third week; and (c) predict how many records Andrew will have during week 30 if this pattern continues. | First, you would need to figure out what the x- values (time) would be from the word problem and in this case 1 to represent the first week and 5 to represent the fifth week. Then pull out the numbers from the word problem that represent the amount which is the y- values and in this case it is 4 and 28. So, altogether the coordinates would be (1,4) and (5,28) which is what is needed to plug into the (y2-y1)/(x2-x1) formula in order to get the m or slope . When you plug in the numbers it should look like (28-4)/(5-1) and when you evaluate you would get 6, so m=6. In order to figure out the linear equation you would use the y=mx+b formula and plug in the slope you found earlier and one of the coordinates preferably the one of the smallest value. So then it would look like 5= 6(1)+b and as a result b= -1, so altogether the formula for the problem would be y= 6x-1, which is the answer for the part A of the problem. Then to find part B, you would plug in 3 in the x place of the y= 6x-1 and would get y= 6(3)-1 which equals 17, so Andrew had 17 records in the third week. To solve for part C, you must extrapolate the data and plug in 30 in the linear equation, so it would be y= 6(30)-1 which is 179 records in the 30th week. | The fixed cost is what is typically paid monthly and it stays approximately the same and it is basically the rent, utilities, advertising and other things. However the variable cost is the cost to make an item and it varies on the items produced. Usually the variable cost is followed with a variable (x). The cost C(x) is represented by adding the fixed costs and the variable cost (x). | The revenue is how much the person charges for each item sold and the profit is the revenue (money made) minus the cost that was used to produce the item. For example, a girl making lemonade can charge $1.50 for a glass of lemonade which is the revenue. The fixed cost to make her stand was 50 cents since she spent it on markers that only work to make the sign and the variable cost was 25 cents to buy sugar for each cup she sold. So altogether the cost was 75 cents to make lemonade and she was charging $1.50. In order to find the profit you would write P(x)= 1.50- .75. | Andrew is starting his own band called MGMT. It costs him $3000 monthly for time in the studio, wages for the other band members, and other expenses and it costs $40 to print out each ticket. He sold concert tickets for $60 dollars for a music festival in Stanford. Write your (a) Cost Function; (b) Revenue Function; (c) Profit Function; and (d) estimate the number of tickets Andrew will have to sell in order to break even. (Round up to the nearest ticket if necessary and find the amount of profit if you do round up.) | In order to find part A, you must identify the fixed cost ($3000) and the variable cost ($40x) and it would be C(x) = 3000 + 40x. To find part B, you find how much he is charging each ticket which is the revenue and it is $60 so the Revenue Function is R(x)= 60x. To find the profit function for part C, you place the revenue function minus the cost and it would look like P(x)= 60x- (3000- 40x) and it would simplify to P(x)= 20x- 3000. To find part D, you would find the break-even point by 20x- 3000= 0 and solve which would give you exactly 1500. So Andrew would have to sell 1500 tickets in order to break even. | USE UNITS when doing word problems. Underline time and amounts in order to make it easier to know what it what. The fixed cost is what is paid monthly and it stays the same. The variable cost is the cost to make an item and it varies on the items produced. The cost C(x) is represented by adding the fixed costs and the variable cost (x). The revenue is how much the person charges for each item sold and the profit is the revenue (money made) minus the cost that was used to produce the item(P=R-C or PRiCe). The Break Even Point (BEP) is the P(x)=0 and round up to the nearest whole unit. REMEMBER to find the profit of the BEP if rounded. | Solving linear equations. | perhaps writing the word problems and the steps to solve them was a little complicated but not too bad. | kenia.garibay@yahoo.com | ||||

64 | 6/19/2013 12:18:28 | Gomez | Rita | To solve a linear problem you have to identify your x, which are the ones which tell time, and your y, the oens that identify the amount. And since yo have to order pairs, you find the slope using the formula. After you find your slope you have to find your b. to do this you plug in one of your pairs into the equation. Finally you have your equation and now you can find other time period and see ehat amout it gives you. | it is what helps you id find more of what the equation gives us. | Agnus is selling bows at the beach. During the first week she sales 10. During her 7 week ,everyone has heard about her cute bows, she sold 40. Assuming her sales follow a linear model.(a) write a linear equation model of her sales;(b) calculate how many bows did Agnus sell in her 5th week. (c) predict how many bows se will sell in the 20th week. | So we have our time and our amount so we put them in pairs by (time,amount) which gives us (1,10) and (7,40). Having this you can plug it in to the slope formula which is y2-y1/x2-x1. which would be 40-10/7-1 = 30/6 = 5. Knowing our slope we will use formula y=mx+b. Plug in a set a pairs 10=5(1)+b. by simplifying we get b=5. Now we have our linear equation which is y=5x+5. know we just plug in the 5 to the equation to find the answer to B. Y=5(5)+5 which at the end equals 30. Similarly, we plug in the 20 to our equation and simplify and it comes out as 105. | There are two types of cost the fixed cost and the variable cost. The fixed cost is the montly cost, whichc really never changes. But the Variable cost is the cost to make your item. | Revenue is how much you charge for you item. While Profit is how much you get out of minus the costs. For example if you are selling a cookie for 5$ thats your revenue, but it cost you 2$ to make it ( 5-2=4) your profit is 4$ per cookie. | Agnus is starting a bow buisness. It costs her $200 for monthly equipment, and $2.00 for supplies for each bow. She sales each bow for 5$. what is her a) cost function b) revenue function c) profit function d) Bep. | To find her cost functions you just have to add both functions which is 200+2x. Their is an x on the two because thats per bow. To find the revenue is real simple you just have to put your cost times the amount but since we have no amount we put x; so it would be 5x. To find our profit we have to subtract our revenue with our cost. Simplifying everything it comes out as 3x-200. We use this to find out Bep. We equal the profit equation an simplify 3x-200=0 which gives us 6.666. Because we cant have 6.666 of a bow we round it up t0 67, which is out BEP. knowing this we plug it back to the profit equation and get 1 (3(67)-200=1) which means 1$ is our amount of profit. | key terms like: First week, third week, monthly equipment, supplies ect. | how to transfer the linear problem to a slope formula. | the BEP and after getting it why do you need to find the profit. | rg.roxy123@gmail.com | ||||

65 | 6/25/2013 14:19:32 | Gomez | Odalys | The first step in solving a linear model is to read through the word problem carefully. The next step in solving them is to figure out your two points. the x would be the time and y would be the amount. After you get your points you solve for the slope using the slope formula. one you have your slope you plug it into y=mx+b. Another thing you plug into the formula is a point you solve it through to get the y intercept therefore having everything you need to make the equation. You then have the equation and can plug in any number to get how much of whatever you want to find in that amount of time. | The word extrapolating means to extend, for example if you are given the week 4 and week 7 you can figure out how much will be in week 76 by using the linear model. | Sandra enjoys playing new video games. She buys video games constantly. She plans on buying video games until she has them all. During the first week she buys 1 video game. By the 7th week she has 13 video games. Assuming she buys video games in a linear model, write the linear equation to model how many video games she has bought; calculate how many video games she bought in week 3; and predict how many total video games Sandra buys by week 20 assuming the pattern continues. | The first thing you do is find the points which are (1,1) and (7,13). The next thing you do is plug in y2-y1 over x2-x1. The answer to plugging that in is 2. The next step is to get the liner equation. The liner equation for those points would be f(x)=2x-1. After that you plug in f(3) to the equation. The answer to that would be 5 video games. Then to calculate the number of video games you plug in f(20). The answer to that would be 39 video games. | The two different type of cost are fixed costs and variable costs. the fixed costs are costs that you would pay monthly and don't change, like rent or utilities. Variable costs can vary, that would be like an amount of something you need to make a sell. An example would be if you sell erases you have to purchase them before you sell them for a profit, and the amount you need one month isn't the same always. | Revenue is just the price you have the item for. revenue is the money you get for an item. Profit is the amount of money you gain from selling the item. this is the revenue minus the costs. For example if your selling books you sell them for a dollar. you sell 8000 books, the costs of this month was 2000 dollars so you subtract 8000-2000 making a profit of 6000 dollars. | Sandra is starting a business. She wants to sell video games because she collected so many. It costs her $1400 for monthly equipment and rental fees, and $.30 for supplies to wrap a video game. she decides to sell each video game for $20 dollars. Write her cost function; revenue function; profit function and estimate the number of video games she needs to sell to break even. | The first equation is the cost equation which is c(x)=1400+.3x. The next equation you do is the revenue equation and that it r(x)=20x. The next step is to figure out the profit equation and that is p(x)= 19.7x-1400. to figure out if you break even you set the profit equation to 0. The answer to that is 71.06 video games but since you cant have .06 video games you round it up to 72 video games and you have a slight profit and that is $18.40. | what the x and ys are in the linear models, the steps to solving it, the definition of cost, revenue profit and break even. and lastly how to solve the problems. | the linear models. they are easy to solve. | how the revenue and the profit are used to find the breaking even point. | gomezodays26@yahoo.com | ||||

66 | 8/26/2013 13:30:29 | Gomez | damian | first you have to figure out the two points with x being the time and y being the amount. Then you must figure out the slope intercept formula. After that you plug in the x value for whatever amount of time is asked. | extrapolating means too continue the line based on the assumption that it follows a linear model | Bob likes to collect pokemon cards for fun. Every week he likes to go buy a few packs at target. The first week of his collecting he has 8 cards that he bought. After 7 weeks he now has collected 92 cards. Assuming this follows a linear model figure out how many cards he by week 5 and predict how many he will have after 22 weeks. | the ordered paris would be 1,8 and 7,92 due to the time and how many cards he has collected. the equation would be y=14x-6. After that you would plug in the 5 and get 64 and thats how many he had after 5 weeks. To get how many he had after 22 weeks you plug that into the equation and would get 302 | fixed costs don't change often and don't have any monthly variables too change them while variable costs have many different variables that are constantly affecting them. they both drive up the break even point. | revenue is the amount of money you make in total by selling items while profit is the money you have left after paying all your costs. | Bob decides to open a store selling various types of cards. He pays 1000 for rent and employees. Each card he buys costs a dollar. He sells each card for 5 dollars . | his cost function would be c(x)=1000,the fixed costs, + 1x, the price that he pays for the cards,. the revenue function would be r(x)= 5x since he charges 5 dollars for each card. His profit function would be 4x-1000. his break even point would be 1000/4 which is 250 | i need to remember the cost revenue and profit functions | linear models | the profit function | gomezdamain41@yahoo.com | ||||

67 | 6/27/2013 21:58:23 | Guerra | Andrea | Step 1: You must find the two sets of ordered pairs. The x-value representing time and the y-value representing an amount. Step 2: Find the slope (m) by using y2-y1/x2-x1 Step 3: Take the slope and an ordered pair and plug it into y=mx+b to solve for b Step 4: Set up the equation with all the new information in a function format [f(x)=mx+b] Step 5: Plug in and evaluate the equations with the time (x) value given | Extrapolate means to estimate what is coming next. For example, if a word problem gives you (1,6) and (5,46), plot those two on a chart to find a reasonable ordered pair associated with the equation. | Bethany creates original handmade bows and sells them. During week 1, she sells 3 bows. During week 9, Bethany slowly makes progress and sells 19 bows. Assuming her ales follow a linear model, (a_ Write the linear equation to model her sales; (b) calculate how many bows Bethany sold during week 4; and (c) predict how many bows she will sell during week 26 if this pattern continues. | Step 1: You must find the two sets of ordered pairs which are (1,3) and (9,19) Step 2: Find the slope (m) so set up the equation and solve for the slope 19-3/9-1= 16/8= 2 (m=2) Step 3: Take the slope and an ordered pair and plug it into y=mx+b to solve for b making it 3=2(1)+b 3=2+b (subtract 2 from both sides) 1=b Step 4: Set up the equation with all the new information in a function format (a) [f(x)=2x+1] Step 5: Plug in and evaluate the equations with the time (x) value given (b) f(4)=2(4)+1 8+1 9 (c) f(26)=2(26)+1 52+ 1 53 | The different costs we have are fixed costs and variable costs. Fixed costs are what are paid the same every month. Variable costs vary on how many items you make, it might not ever be the same. | Revenue is how much you charge. While profit is what remains of the revenue when costs are subtracted. An example of a revenue: A book costs 6.50 dollars so the function is R(x)=6.50x. An example of profit: we already have the cost and revenue functions: C(x) = 3.50x + 1200 dollars (Daily cost to make x books) and R(x) = 6.50x dollars (Revenue from the sale of x books) so the equation would be P(x)= 3.50x-1200 dollar.s | Bethany is starting a bow business. It costs 1000 for monthly equipment and rental fees, and $1.75 for each bow. She sells each bow for $3. Write a (a) Cost Function; (b) Revenue Function; (c) Profit Function; and (d) estimate the number of bows she will have to sell to break even (round up to the nearest bow if necessary and find the amount of profit if you do round up.) | Step1: set up the Cost Function (a) C(x)=1000+1.75. Step 2: setup the Revenue Function (b) R(x)=3x Step 3: set up the Profit Function (c) P(x)= 3x-(1000+1.75x) {make sure to distribute the negative} 3x-1000+1.75x P(x)=2.25x-1000 Step 4: Set the Profit Function equal to zero and solve for the BEP 2.25x-1000=0 +1000=+1000 {add 1000 to both sides} 2.25x=1000 {divide 2.25 from both sides} x=445 bows (the BEP) Step 5: Plug the BEP (445) into the Profit Function to find the profit p(445)=2.25(445)-1000 1001.25-1000 $1.25 | Revenue is how much you charge. Profit is what remains of the revenue when costs are subtracted. P=R-C | I understand all of both concepts. | I am not confused on either concept | dreashorses@sbcglobal.net | ||||

68 | 8/20/2013 16:45:17 | Guerrero | Jennifer | The first step is to find the x (time) and y (amount). Then set them in parenthesis and do the a, b, and c. For a you have to use the formula to find the slope. For b you have to find the f(x). Finally you have to plug in the amount of c. | The word extrapolating means to extend. For example, when graphing you have to go further more to find out the extra information. | Bryan sells shoes in the mall. During, week 1, he sold four shoes. During, week 6 he sold 34 shoes. Assuming his sales follow a linear model . (a) write the linear equation to model his sales; (b) calculate how many shoes he sold in four weeks; and (c) predict how many shoes he will sell by week 48. | (1,4) (6,34) find x and y a) 34-3=30 6-1=5 then subtract the y and then the x 6= the slope and plug it into a line equation then plug a parenthesis which gives you y=6x-2 then plug 4 into x and you get 22 then plug 48 into x you get 286 | The two different types of cost are fixed cost and variable cost. Fixed cost is what's paid monthly and its the same amount such as rent, utilities, and advertising. Variable cost is how much it costs to make each item. | The difference between revenue and profit is that revenue is how much is charged for each item sold. Profit is when you take your revenues and subtract your cost. For example the revenue if you sell shoes for 40 dollars and profit is the revenue and the cost by using shoes. | Bryan is starting a shoe business. It costs him 1500 for monthly equipment and rental fees, and 20 dollars for supplies for each pair of shoes. He sells each pair for 40 dollars. Write the (a) Cost function. (b) Revenue Function. (C) Profit function (d) estimate how many shoes he has to sell in order to break even. | First you have to find the c(x) which is 1500+20. Then r(x) which is 40x. After the p(x) which is 40x- (1500+20). Finally set it to zero and you get two because you round which its your profit. | The most important facts terms, and tips I need to remember from these concepts are cost, profit, and revenue. | The part that I understood most from these two concepts are the linear models. | The part that I'm still a bit confused on is the cost, profit, and revenue problems. | jenniferguerrero76@yahoo.com | ||||

69 | 6/24/2013 20:05:21 | Gutierrez | Rebecca | You first have to find the slope by the two ordered set pairs. The Then you plug in one of the ordered pairs into slope intercept formula to find the equation of the problem. Next you just plug in the number they ask for time into the equation as if you were evaluating a function. | Extrapolating means that you are guessing how much something would increase based on two amounts that you already have. | Jai love making tie dye shirts and his friends where always asking him to make shirts for them. He decided to make a side business and sell them to his friends.During week 1, he is able to sell 5 shirts. During week 10. his shirts have gotten around and sells 50. Assuming his findings follow a linear model, (a) write the linear equation to the model his sales; (b) calculate how many shirts Jai sold during week 5; and (c) predict how many shirts he will sell during week 35 if this pattern continues. | First you must find your set of ordered pairs which in this case is (1,5) and (10, 50). Then from those numbers calculate the slope which is 5. Then from there to find the equation for (a) you use slope intercept formula and plug in one of the ordered pairs. After plugging the number the equation end up being f(x)=5x+5. To figure out (b) you just plug in 5 into the equation to find out how many shirts he sold in that week and turns out to 30 shirts. Then the same goes for (c) you just plug in 35 into the equation to extrapolate how many shirts were sold in that week which was 180. | The two different cost we have is the fixed cost and the variable cost. The fixed cost is how much money a business will pay regularly for electricity gas and other things of that sort. The variable cost is how much money it takes to make a product and it varies because you won"t always make a consist amount of a product because it won"t always be in demand or other factors. | Revenue and profit are both ways you are making money but in two different senses. Revenue is how you make when the cashier get a customer and money is brought in. However, profit is the amount of money you actually make after you pay off your fixed and variable costs. | Jai has started his own tie dying business. It costs .him $3500 for monthly equipment and rental fees, and $3 for supplies for each shirt. You sell each shirt for $10. Write your (a) Cost Function;(b) Revenue Function; (c) Profit Function; and (d) estimate the number of shirts you will have to sell in order to break even ( round up to the nearest shirt if necessary & tell how much profit you will make if you have to round up). | First you have to find your (a) Cost function which is the fixed costs ($3500) plus you variable costs ($3) which would turn out to be C(x)=3500+3. Then find your revenue costs which would be how much you sell your product for which for this would be R(x)=10x. Then profit cost will be the revenue cost minus the cost function which will be P(x)= 7x+3500.Then to find your BEP You set that equation equal to zero and solve for x to find the amount of shirts you need to sell the break even which turns out being 500 shirts and you break even exactly. | I need to remember from these concepts is understanding the differne between both process. | The part i understood most is being able to extract the neded information to plug into the formulas. | I am not confused about any part. | beckygutierrez0@yahoo.com | ||||

70 | 6/28/2013 13:59:15 | Gutierrez | Emmanuel | To solve a linear word problem, first you must extract two sets of ordered pairs from the word problem, where x represents time and y represents amount. Then you must find the slope of the line using the two sets of ordered pairs. After that, you plug-in x and y to the y=mx+b equation to find b. That's how you get your linear equation. If they then ask you to calculate or extrapolate an amount, you just plug the time(x) in and simplify. | Extrapolating means to predict an amount(y) on a linear equation if you already know what the linear equation is. For example, if you know that a problem's linear equation is f(x)=5x+3, and you want to extrapolate to find f(13), then you just plug-in 13 for x and simplify. Which gives you 68. | Julian loves playing marbles. He begins a collection of rare marbles, which he wishes to sell in the future, when their value increases. During the first week, Julian collects 7 marbles. During the sixteenth week, he had expanded his collection to 67 marbles. Assuming his collection follows a linear model, (a) Write the linear equation to model his collection; (b) calculate how many marbles Julian had in his collection during the eighth week; and (c) predict how many marbles Julian will have during the twenty-fifth week if this pattern continues. | 1. You must extract two sets of ordered pairs from the word problem (1,7) and (16,67). 2. You must find the slope of the linear equation by using y2-y1 over x2-x1(m=67-7 over 16-1, m=60/15, m=4). 3. Plug-in (1,7) to y=4x+b to find b [7=4(1)+b, b=3] 4. Write the linear equation [f(x)=4x+3] 5. Plug-in f(8) to find Julian's marble collection during the eighth week [f(8)=4(8)+3, f(8)= 32+3, f(8)=35] 6. Plug-in f(25) to find his marble collection during the twenty-fifth week [f(25)=4(25)+3, f(25)=100+3, f(25)=103] | The two types of cost we have are Fixed and Variable costs. They have the same equation, which is C(x)= fixed+variable cost(x). Fixed cost is something that's paid monthly ans stays the same every month, while variable costs are how much it costs to make each item. Fixed costs include: rent, advertising, utilities, but variable costs vary based on quantity. | Revenue is how much you charge for each item you see. On the other hand, profit is how much money you make after subtracting costs by the revenue. A real life example is if you own a pencil shop. Revenue would be how much you charge for each pencil($1). Profit is the money you make after paying your costs with the money you brought in. | Julian is starting a marble selling business. It costs him $2000 monthly equipment and rental fees, and $1 for supplies for each marble bag. He sells each marble bag for $5. Write your (a) Cost function; (b) Revenue function; (c) Profit function; and (d) estimate the number of marble bags you will have to sell to break even(round up if necessary and find profit if rounded) | 1. Find the cost function by adding the fixed and variable costs [C(x)=2000+x] 2. Find the Revenue function by finding the charge of the item being sold [R(x)=5x] 3. Find the Profit function by subtracting revenue by cost [P(x)=(5x)-(2000+x), P(x)=4x-2000] 4. Find the Break-Even Point by putting the profit function equal to zero [4x-2000=0, 4x=2000, x=500 marble bags] | Cost, Revenue, Profit, Break-Even point, extrapolate, word problems, linear equations, and PRiCe. | writing and solving cost, profit, and revenue word problems. | writing linear word problems. | gutierrezemmanuel35@gmail.com | ||||

71 | 6/28/2013 23:42:17 | Hang | Jade | In solving a linear model word problem, we first have to read through and find the time, which would be the x-value, and the amount, which would be the y-value. To solve for the equation, we would need to find the slope using the ordered pair from the numbers we collected from the problem (y2-y1)/(x2-x1). Then we would plug in the numbers for y=mx+b, using the numbers from the problem to plug in x, y, and the discovered slope, which will lead us to find b and ultimately our equation. Our word problems ask for two more times, which we would solve by plugging into our equation. | Extrapolating means to go beyond the given amounts, and find the amount number if the pattern of the linear model continues with the pattern. An example of could be finding the amount of chocolate bars sold after 7 weeks, when we know that 1 week would sell 25, and 5 would sell 120. | Sam started to sell boxes of cupcakes. The first week she sold 6 boxes to her friends. By the 5th week, she had sold 42 boxes in total. Assuming her sales follow a linear model, (a) write the linear equation to model the number of boxes she has sold; (b) calculate how many boxes Sam had sold by week 3; and (c) predict how many total boxes she will sell by the end of week 10, assuming this pattern continues. | First we would find our two ordered pairs, and in this case, the two x-values (which represents time) would be 1 and 5. Then we find the two y-values (which represents amount of boxes sold), which would be 6 and 42. We would put these numbers into their ordered pair: (1, 6) and (5, 42). Using this, we would find the slope of the equation first, using the slope function (y2-y1)/(x2-x1). In this case, it would be (42-6)/(5-1), which would equal 36/9, and simplifies to 9. Part A asks for us to find the linear equation (y=mx+b). Using the smaller numbers and the slope we found, we plug in the numbers to find be (6=(9)(1)+b). We find that b equals -3. The linear equation for this problem is y=9x-3. Part B asks to find how many boxes Sam sold by the end of week 3. So we would plug in 3 into the equation y=9(3)-3. The answer would be 24 boxes. Part C asks to find how many boxes Sam will sell by the end of week 10, if the pattern continues. So like part B, we plug in the number to get y=9(10)-3, which equals 87 boxes | There are two different types of cost: fixed and variable. The cost function is C(x), which is broken down into those two parts. The fixed costs are what business people pay monthly, constant rate. The variable costs are how much it costs to make each item. This would differ from fixed costs because the amount of sales is not always constant, unlike those of the fixed costs. | Revenue is how much a business charges their products, while a profit takes away from how much it cost to make the product. The equation for revenue would be R(x)=____(x), and the equation for profit would be P(x)= R(x)- C(x), x being the number of products. An example of a revenue would be a toy business selling their product for $15. An example of a profit would be taking that revenue, and subtracting how much it took to make the toy: $15-$7= $8. The $8 would be the business's profit. | Sam had started her own business selling cupcakes iin her new bakery. It costs $2500 for monthly equipment and rental fees, and $9.25 for supplies for each box of cupcakes. She sells each box for $15. Write your (a) Cost Function; (b) Revenue Function; (c) Profit Function; and (d) estimate the number of boxes of cupcakes she will have to sell in order to break even (round up to the nearest box if necessary and find the amount of profit it you do round up.) | We first start with part A, which is finding the cost function. The cost function included the fixed and variable cost. In the problem, we know that the fixed cost is $2500 and the variable cost is $9.25. The cost function would be C(x)= 2500+ 9.25. Next we solve for part B, which asks us to find the revenue function. This would be R(x)=15x. We then solve for the profit function in part C. The profit function in every situation is P(x)= R(x)- C(x), so we plug in what we already found. It would lead to: P(x)= 15x-( 2500+ 9.25x). First we would distribute the minus to the parentisized part, and then simplify. This would give us P(x)= 5.75x-2500. After we find the profit function, we go on to part D, which asks us to find the break-even point, or BEP. In order for us to do this, we equal the profit function to 0, which would be 5.75x-2500=0. We would add 2500 to both sides to get 5.75x=2500. To get x by itself, we divide 5.75 from both sides, making x= 434.78. Because x is not a whole unit, we need to round up to the biggest number, making the BEP 435 boxes. To find the profit, we plug in 435 into the profit function, which would give us a profit of $1.25. | For linear problems, x-value represents time, and y-value represents an amount. Cost are divided into two sections: fixed (constant) and variable (inconstant). Its equation is C(x)= fixed+variable(x) Revenue is how much a business charges for its product. Its equation is R(x)= Profit is taking the revenue and subtracting the costs. Its function is P(x)= R(x)- C(x) Break-even point is whether a business is not losing money, or gaining money. The BEP must be a whole unit. To find the BEP, we would either use P(x)=0, or R(x)= C(x) | solving cost, profit, revenue, and break-even points. | All concepts are completely understood. | jadekimhang@yahoo.com | ||||

72 | 6/29/2013 0:11:16 | Harker | Rebecca | With the given points find the slope using the slope formlua. Once the slope is found plug it along with a point to find b, the y-intercept, to solve for the equation. If it asks you for a certain number to solve the equation for the number by plugging it into x and simplifying. | Extrapolating means to estimate. Like in number 3 in lesson 7. | My brother loves to make movies. During 1st week of his college career he made 3 movies. During is 13th week of school, he got really bored so he decided to make 87 movies. Assuming his movie making skills follow a linear model,(a) Write the linear eqation to model his starfish colection. | First, I would find the points which are (1,3) and (13,87). Then, I would plug them into the slope formula and solve. After that I would plug the slope along with a point into y=mx+b to solve for b. Then you have your answer. | Fixed costs are paid monthly and stays the same every month. While variable costs is how much it costs to make each item. | Revenue is how much you charge for each item you solve. Profit is when you take your revenue and subtract your costs. | My brother has decided to make a business out of his movies. It costs him $1500 for monthly equipment and rental fees, and $3.25 for each disc. He sells each movie for $14. Write your cost function. | I would find the fixed value for the cost funcion and find the variable cost and plug it into the equation. | The most important facts, terms, and tips I need to remember from these three concepts are to remember how to write and solve cost profit and revenue word problems | The part I understood the most from these two concepts is writing linear models. | The par I am still confused about is how to solve cost, profit and revenue problems. | rtharker97@gmail.com | ||||

73 | 6/28/2013 21:02:47 | Jogwe | Nnamdi | First find the slope by subtracting the latest y from the earlier one and then do the same process for x. Then divide the answer for y by the answer for x to receive the final slope. With the slope plug it in for any given x value and the difference from the plugged in answer with the actual y value gives "b" in the y=mx+b formula. | To continue a series based on the given information but maintaining the same values. If the points (1,3) and (3,5) are given then a continuation would mean (100,102) would be a point on the graph. | The fetus was deciding if it should become a male or female when it should be born. The fetus compiled three reasons on why it should be a male with Xy chromosome. The fetus then thought of 15 reasons why it should be a male after a week. Write a linear equation that would determine the amount of reasons the fetus would want for being male. Also if the line continued determine how many reasons the fetus would have after 11 days. | First determine the points which would be (1,3) and (7,15). Then figure out the slope. 15-3=12. 7-1=6. 12/6=2 so m=2. Plug in 2 to any of the points. 7(2)=14. 15-14=1 so b=1. Therefore y=2x+1. Then for the second answer plug in 11 to the slope intercept equation. 11(2)=22. 22+1=23. | The two different types of cost include fixed costs and variable costs. Fixed costs mean that they are the same for every time unit. This is because they are usually utilities such as rent or utilities. Variable costs are the second form of costs. They have a rate for the cost to make a certain item which is the rate and stays the same. Although the amount of items made changes every time. | Revenue connotes to how much is charged for each item. The equation would be R(x)=__(x). A real life example would be the $5 dollars that a wearable towel is sold for. The profit is the amount of money made. The profit is found by subtracting the revenue from costs. The equation is P(x)=R(x)-C(x). A real life example would be the $10 that beanie babies made this year. | The fetus figured out that genetically it was going to bald early in the future. It then created the product of spray on hair. It costs $1200 a month for equipment and rent. It costs $1.50 for each of the items for an individual can of spray on hair, but it is sold for $3 each. Write the following: cost function, revenue function, profit function, and estimate for the break even. | A) First find the fixed cost which is $1200. Then find the variable cost which is $1.50. The cost function would then be C(x)=$1200+$1.50. B) The fetus decided to sell each can of spray on hair for $3 so the revenue function would then be R(x)=$3. C) For the profit function subtract the amount that the cans are being sold for by the amount that each can costs. This is 3-1.5=1.5. Then that sum is subtracted by the fixed cost for the profit function being: P(x)=1.5x-1200. D)Set the profit function equal to 0 to find the BEP. Move the 1200 to the opposite side then divide it by 1.5. This leaves $800 for the BEP. | They would be extrapolate, fixed cost, variable cost, revenue, profit, and break even point. | The part I understood most was the cost function. | I fully understood the concepts. | jogwennamdi@yahoo.com | ||||

74 | 6/29/2013 0:20:18 | Khan | Sabrina | The first step in solving a linear model word problem is to set up two ordered pairs with x representing time and y representing amount. For example (week #, books sold). The next step is that after you have found the ordered pair, now its time to create a linear equation. To do that you must first find the slope between the coordinates (y2-y1/x2-x1). Once you have found the slope you plug it in for m and then you plug in any coordinate into the equation to find b. Once you solve the equation to find b you have your linear equation (y=mx+b). | The word extrapolating means to expand and predict a value using the information that you already have. For example, if Lulu the panda eats 100 bamboo sticks the first week at the zoo and then 500 sticks on her 6th week at the zoo we have to extrapolate and use this information to figure out how many sticks Lulu will eat in total by the 18th week. *This is only if we assume that her eating pattern is linear*. | Lulu is a baby panda that just moved to the San Diego Zoo. Lulu also loves to eat. On her first week at the zoo, Lulu ate 100 bamboo sticks. By her sixth week at the zoo Lulu had eaten a total of 500 bamboo sticks. Assuming that her diet follows a linear model (a) write the linear equation to model the number of bamboo sticks Lulu ate (b) calculate how many bamboo sticks she ate during week 3 and (c) predict how much bamboo sticks Lulu will eat during week 18 if this pattern continues. | First with the given information, you have to set up two sets of ordered pairs. So the information needed would be (week#, bamboo sticks). So the first pair is (1, 100) and the second pair would be (6,500). Now that we have our ordered pair we have to find the slope in order to create a linear equation. So to find the slope it would be 500-100/6-1 which would be 400/5=80. So the slope (m) is 80. Now that we have the slope we can find the b. To do that we choose a ordered pair and make the equation: 100=80(1)+b. When we solve it b would equal 20. So the linear equation is f(x)=80x+20. Now to do question b we would plug in f(3) into the equation: 80(3)+20=260 bamboo sticks. so the answer for b is 260. To do part c you would plug in f(18) into the equation so f(18)=80(18)+20=1,460. So the answer for c is 1,460 bamboo sticks. | The first type of costs are fixed costs which are things such as house rent, utilities, etc. These costs are paid monthly and stays the same every month. The variable costs on the other hand is the cost of how much it costs to make each item. Variable costs are not constant and they vary each month. These costs are determined on how many items you want to produce. | Revenue is the money you bring in. It is how much a company charges for each item that they sell. For example, a T-shirt company that sells their shirts for $10 then their revenue would also then be $10. A profit is what's left after you subtract the revenue from the costs. So if a t-shirt company gets a revenue of $100 then they have to subtract that amount from the costs which let's say is $75. Therefore, the company would make a profit of $25. | The San Diego Zoo wants to start a selling tickets for their new panda exhibit (staring the rare, adorable baby panda Lulu). It costs the zoo $1500 a month for the exhibit's utilities, advertisements, and to take care of Lulu (she's a diva) and $1.50 to make each ticket. Each ticket is sold for $10. Write the (a) cost function, (b) Revenue function, (c) profit function. In addition estimate the number of tickets the zoo will have to sell in order to break even. | First we need to find the costs: the fixed costs and the variable costs. The fixed costs are the costs that are paid monthly so it would be $1500. The variable costs are the costs that take to make each item so it would be $1.50. The equation for the costs is fixed cost +variable costs(x). So c(x)=1500+1.50x. The revenue would be R(x)=10x because the zoo brings in $10 for each ticket sold. The profit would be the revenue minus the costs. So the equation would look like (10x)-(1500+1.50x). When you solve it would be p(x)=8.50x-1500. To find the break even points you set the profit-p(x)-equal to zero. So it would be 8.50x-1500=0. (to solve: add 1500 to both side: 8.50x=1500) and the x would equal 176.47. Remember that for the BEP you have to round up so the BEP must be 177 tickets. | The most important things I need to remember are the terms and equations for the business problems. I have to remember the difference between the fixed costs and variable costs and the equation for the cost. I also have to remember that the equation for profit is R(x)-C(x). | The part I understood the most from these two concepts is concept #6. At first I was intimidated when I saw word problems (they're not my favorite) but after the first problem I immediately understood it :). I got all the steps down in order to create a linear equation from the word problem and to predict something from the information in the word problem. It was very easy for me to create my own problem and to solve it step by step. | Honesty, there is nothing really that I am confused about in these two concepts. At first I was confused about what it means to extrapolate but then I rewatched the video and then I understood it. | sabrinakhan913@yahoo.com | ||||

75 | 6/28/2013 16:49:04 | Larco | Daisy | To solve a linear model problem first you must set up two sets of ordered pairs, where the x value will represent time and the y value will represent an amount. From those two sets you must retrieve the slope using the slope formula. Then after you have a slope you must then write n equation.After that you basically use the equation as a function and plug in the week number or what you are looking for. | To extrapolate means to assume and go past what you are given to see or retrieve data from a future time. | Delylah loves flowers. She owns a flower shop called D's Flowers in costa mesa. In her first month of opening her shop she sold 16 bouquets of flowers. By the 6th month she had sold a total of 61 bouquets of flowers. Assuming her sales follow a linear model (a)write her linear equation to model her total flower sales (b) calculate how many flowers Delylah would have sold by the 9th month (c) predict how many total flowers Delylah will have sold by the 16th month if the pattern continues. | First you must write your two equations you get from the world problem. In this case the two problems you have are (1,16) and (6,61). With those two points you use the slope formula and once you do the math you end up with 9. With the number 9 you plug it into the formula y=mx+b. Also with the 9 you plug in an ordered pair. For example I am going to plug in 9 and the first point we have like this----> 16=9(1)+b when we solve we get b=7 so our formula is y=9x+7. Once we have this formula we can plug in what we are trying to look for. it is easier if we set it up as a function, like f(x)=9x+7. so we are looking for the sales amount by the 9th month so we plug in 9 like this f(9)=9(9)+7 and we get 89 bouquets of flowers. They are also asking for the 16th month is the pattern continues so we plug in 16 and get f(16)=9(16)+7 and we get 151 bouquets of flowers. | There are fixed costs which are the amounts that stay the same every month and do NOT vary such as rent. There are also variable costs which do vary by the amount of the item you are selling. For example say you own a t shirt shop the amount it costs to make them a month varies because the amount of t shirts you make a month varies. | Revenue is the amount at which you charge for each item you are selling. For example revenue is the actual money earned. Profit is directly related to the item or product . It made up of your revenue minus your costs. Also profits usually how much money a person or company makes while revenue is the money coming in for that product. | Delylah started her own flower business. It costs her $1600 for monthly rent and equipment fees, and $1 for each flower. She sells each flower at $4. Write her (a) cost function (b) revenue function (c) profit function (d) estimate the number of flowers she will have to sell in order to break even (round up to the nearest flower necessary and find the amount of profit if you do round up. | For a we have the total costs plus the variable costs which is C(x)=1600+1x. for b we have the revenue which s r(x)=4x for c we have profit which is the revenue minus the fixed costs plus the variable costs. which is p(x)=3x-1600 for d we must find the BEP . to do that we set our profit equation to zero. once we complete the math we end up with 533.33 flowers but then we must round to 534 flowers and if we plug f(5340=3(534)-1600 we end p with a small profit of $2. | I must understand the definitions and how to get cost revenue profit and BEP from a word problem. | The part I understood the most was writing the linear models and evaluating for word problems. | The part I am still confused about the most from these two concepts is writing and solving cost profit and revenue word problems. | nmdl11@ahoo.com | ||||

76 | 6/26/2013 18:31:38 | Le | Phuong | First step is to plug in the numbers into (Week #, #of items). Then solve for the slope of those points. Solve for B. then plug it into f(x)=10x-4. | Extrapolating means to estimate or figure out the amount of something beyond the points given already. For example, if they give you a pattern for weeks one to week 5, finding out what week 9 would be would be extrapolating. | Kim babysits for her neighbors and friends. During her first week of babysitting, she gets $30. By her 8th week of babysitting, she's earned $180. Assuming she gains money following a linear pattern, (a) write the linear equation to model the money she's earned, (b)calculate how much she's earned by week 6, (c) predict how much she'll have by week 15. | (a) Kim had 30 dollars in her first week of babysitting and 180 dollars by her 8th week, making the points (1,30) and (8,180). The slope of this would be 30. To find B, (30)=(30)(1)+b. B equals 0. The equation is now y=30x+0. (b) Plug the value into the x. f(6)=30(6)+0. f(6)=180. (c) Plug the value into the x. f(15)=30(15)+0. f(15)=450. | The two different types of costs are the fixed and the variable. Fixed is the certain amount of money for something, usually used for the amount paid monthly, such as the rent. The variable is how much it costs to make an item. | Revenue is how much you charge for each item you sell. Profit is the difference between the revenue and the cost of making that item. For example, the revenue of a pencil I sell could be $0.75. The profit of it would be $0.25, if it cost $0.50 to make each pencil. | Kim decided to make little crafts for her babysitting jobs. It costs her $1100 for monthly equipment and rental fees, and $2 for each craft bag. She sells them at her babysitting jobs for $5. Write the (a) cost function, (b) revenue function, (c) profit function, and (d) estimate the number of craft bags she'll have to sell to reach break even. | (a) $1100 is the fixed cost and $2 is the variable, so C(x)=1100+2x (b) She charges $5 so R(x)=5x (c) subtract the cost from the revenue. (5x)-(1100+2x)= P(x)=3x-1100. (d) 0=3x-1100 1100=3x x=366.6 P(366.6)=3(366.6)-1100. Profit= $1. | The different equations for each step in solving. | the difference between each different step (cost, revenue, profit, break-even point) | I'm not confused about any part. | phuongnghi15@yahoo.com | ||||

77 | 6/26/2013 23:03:06 | Le | Christine | First, translate the time and amount into two ordered pairs. Find the slope of the line by using the numbers in the ordered pairs and then plugging them into the equation m= (y2-y1) / (x2-x1). Take the slope and an ordered pair and plug it into the slope-intercept form, y=mx+b. Solve for 'b'. Write out your linear equation. Take your linear equation and plug in the number it tells you to calculate in your x-value spot. If it tells you to predict, plug in the number it tells you to calculate in your x-value spot. Remember to write the units. | Extrapolating means to assume/predict the pattern continues. Lets say we had a linear equation of f(x)= 1x +2. If it tells you to predict how many chocolate bars Willy Wonka will have sold by the end of 10th week, you would plug in 10 into the x-value spot (f(x)=1(10)+2) and get a value of 12 assuming that the pattern of the linear model continues. | Christine loves drinking green tea lattes. She has a secret obsession with green tea lattes and can't get enough of them. During her first week at the cafe, she drank 10 green tea lattes. By the sixth week, she drank 120 green tea lattes. Assuming her obsession with drinking green tea lattes follows a linear model, a) write the linear equation to model her drinking obsession; b) calculate how many lattes Christine drank during week 10; c) predict how many lattes she will drink during week 20 if this pattern continues. | First, translate the time and amounts into ordered pairs. The problem states that Christine, during her first week, drank 10 lattes. (1,10). During her sixth week, she drank 120. (1,120). Plug this in to m= (y2-y1) / (x2-x1) (m= (120-10) / (6-1)) to get your answer 22. Take m=22 and an original ordered pair (I will be using the ordered pair (1,10) because it has the more simpler numbers) and plug it into the equation y=mx+b. (10=22(1)+b). Solve for b to get -12. Take your 'm' and 'b' to write your linear function f(x)=22x-12. This is your answer to letter a). For letter b), you will be taking the number 10 and plugging it into your linear equation to find out how many lattes she drank during week 10. f(10)=22(10)-12. You should get the answer 208 green tea lattes. For part c), you would extrapolate and predict how many lattes Christine will drink during week 20 if the pattern continues. Take 20 and plug it into the linear equation. f(20)=22(20)-12 to get 428 green tea lattes as your answer. | There are two kinds of costs: fixed costs and variable costs. Fixed cost is paid monthly. It stays about the same every month. Variable cost is how much it costs to make each item. It varies monthly based on how many items you decide to produce. | Revenue is how much you charge for each item you sell. Profit is how much you gain from the products you sell. Take the revenue and subtract it to your cost to get your profit. Lets say that the chocolate bar costs $2 to make and I sell the chocolate bar for $3. The price I sell the chocolate bar for ($3) is the revenue. To find the profit, I take my revenue ($3) and subtract it to my cost ($2) to get my profit of $1. | Christine is starting a green tea latte selling business. It costs her $1400 for monthly equipment and rental fees, and $2 for supplies for each green tea latte. She sells the green tea lattes for $4. Write your a) Cost Function, b) Revenue Function; c) Profit Function; and d) estimate the number of lattes she would have to sell in order to break even (round up to the nearest latte if necessary and find the amount of profit if you do round up). | Take the costs (fixed and variable) and plug it into teh equation C(x)=fixed costs + (variable costs)(x). So for the problem, we would take $1400 (her fixed cost) and $2 (her variable cost) and plug it into the equation that should look like, C(x)=1400+2x. This is the answer to part a. Then, take the revenue price and plug it into the equation R(x)=__x. It should look like R(x)=4x. This is the answer to part b. For part c, you would plug 'a' and 'b' into the equation, P(x)= R(x)-C(x). It should look like P(x)=(4x)-(1400-2x). Simplify your answer to get 2x-1400. This is the answer to part c. For part d, you would take your profit function and make it equal to 0. Simplify the function to get x=700 green tea lattes. Christine would need to sell 700 green tea lattes to break even. | The x-value will always represent time. The y-value will always represent an amount. 1) translate into ordered pairs. 2)m=(y2-y1) / (x2-x1) 3) y=mx+b; solve for b 4)write linear function 5) plug in and simplify ! The cost equation is C(x)=fixed costs + (variable cost)(x). The revenue equation is R(x)=__(x). To get my profit, take the revenue and subtract it to the cost. Round up yo the nearest object if necessary and find the amount of profit if rounded up. | The part I understand the most from these two concepts is finding the linear functions and plugging the numbers in to solve the word problem. | I understand these two concepts fairly well. | christinele097@gmail.com | ||||

78 | 7/7/2013 18:44:49 | Le | Hannah | First you would have to form two sets of ordered pairs of the time and amount. Then from the ordered pairs, you find the slope of it by using the slope formula and then solve for y=mx+b. Once you find the linear equation to the model, you plug in any number to x it asks for. | It means to the extent of that same amount but different times. Such as if i had 5 books by the end of the 1st week, and 10 books by the end of the 2nd week, how much would i have by the end of the 4th week? | Lola loves collecting stamps from different areas of the world during her free time. During week 1, she collected 10 stamps when she traveled with her mom to California. During week 6, she collected 40 stamps when she traveled to Vegas. Assuming her collection follow a linear model, (a) Write the linear equation to model his stamp collection (b) calculate how many stamps Lola collected during week 7, (c) predict how many stamps she will have during week 80 if this pattern continues. | First you get the ordered pair (1,10) (6,40). Then you use the slope formula and get 6. Then the slope intercept formula 10=6(1)+b. Then b=4 so y=6x+4. Then you would plug in f(7)=6(7)+4 which is 46. So in week 7 she would have collected 46 stamps. Then plug in f(80)=6(80)+4. Which is 484. So week 80, she would have collected 484 stamps. | Fixed costs is when it's paid monthly so usually stays the same every month like rent and utilities. Variable costs is how much it costs to make each item. The cost varies monthly based on how many you produce. | Revenue is how much you charge for each item you sell. Such as if it costed me $2 to make and i sell it for $3, that would be the revenue. Profit is how much you make from it with your revenues in it. So since it costed me $2 to make and sold it for $3. i profited $1. | You are starting a stamp selling business. It costs you $20 for monthly equipment and rental fees, and $.25 for supplies for each stamp. You sell each stamp for $.75. Write your (a)Cost function (b) revenue function (c) profit function; and (d) estimate the number of stamps you will have to sell in order to break even. | the cost function would be $20 + $.25x because thats how much it would cost for each one. Then the revenue function would be .75 because thats how much you are selling it for. The profit would be .75x-20-.25 x which equals to .5x-20. Then you set it up to 0 and would equal 40 and that would be your profit. | Cost revenue Profit and BEP and what it stands for. And to set up 2 ordered pairs for the linear models. | Everything | nothing | elhannah21gmail.com | ||||

79 | 6/28/2013 3:42:17 | Leal | Sarahi | You first separate time and the amount. Time is the x-value and amount is the y-value. After you get your two points, you find the slope. After getting your slope, you pick a point and get the slope and put it into slope-intercept form. After distributing, you get "b" and then you get your linear equation. You then plug in what ever number into "x" in the linear equation and you get your answer. | Extrapolating means estimating the values within a known range by assuming that the estimated value follows the pattern from the known values. For example, if I my grade keeps on increasing each week by three percent, in two weeks I would probably still be increasing my grade by three percent. | Sarahi has an obsession with Korean Pop. She is also so in love with many Korean boy idols that she can't stop adding them to her list of marriage. During her first week of her discovery of KPop, she began her list by adding two Korean boy idols on her list. By the nineteenth week, she had 56 Korean boy idols on her list of marriage. Assuming her love and obsession for Korean boy idols follows a linear model, a) write the linear equation to model her obsession with Korean boy idols; b) calculate how many Korean boy idols were on her list during week 21; c) predict how many Korean boy idols are on her list during week 57 if this pattern continues. | First, you separate the time from the amount. The weeks are the x-value and the Korean boy idols are the y-value. The first point would be (1,2) because in her first week she added two Korean boy idols to her list of marriage. The second point is (19,56) because in her nineteenth week she added fifty-six Korean boy idols to her list of marriage. Then to find the slope, you subtract 56 and 2 and get 54 as your numerator; and after subtracting 19 and 1, you get 18 as you denominator. 56 divided by 18 turns to 3, which is now your slope. You pick one point and get your slope and you plug it in into slope-intercept form. After plugging everything in, "b" equals negative one. So now you have f(x)=3x-1 as your linear equation. To find how many Korean boy idols she had on her list of marriage, you plug in 21 into x's place in the linear equation and you get 62 Korean boy idols. Finally, to see how many Korean boy idols she has on her list of marriage in week 57, you plug in 57 in the linear equation and you get 170 Korean boy idols on her list of marriage. | Fixed costs is different from variable costs, because fixed costs stay constant; while variable costs depends on how much it costs to make the item. With fixed costs you know how much you will have to pay, but with variable costs you don't know the outcome every time. Both fixed costs and variable costs are similar in that they can break or increase your wealth, since with the variable costs you can control how much you want to pay and with fixed costs you are able to know every how much you have to save. | Revenue is how much you charge for each item you sell while profit is when you subtract revenues from your costs and what ever is left ifs your profit. With profit, what ever is left you keep, but with revenue you just sell. An example from real life is when you sell shoes, which is the revenue, you charge the customer when they buy the shoes. Once you sell the shoes, you get the revenues and you subtract it from your costs, which is the profit. If you sell the shoes for a good price, you can earn a great profit from it. | Sarahi's obsession with Korean Pop has gotten stronger when she was able to go to Korea and stay there for over a year! But to pay her bills, she starts a jacket business. It costs her $2100 for monthly equipment and rental fees, and $0.75 for supplies for each jacket. Sarahi sells each jacket for $45. Write her a) Cost Function; b) Revenue Function; c) Profit Function; and d) estimate the number of jackets she will have to sell in order to break even (round up to the nearest jacket if necessary and find the amount of profit if you do round up.) | Sarahi's fixed costs is $2100 and her variable costs are $0.75. Making it "C (x)= 2100+.075x". Her revenue being $45, making it "R (x)= 45x". Now you have to take the revenues and subtract it from her costs, making her profit "P (x)= 44.25x+2100". Now you get her profits and equal it to zero. You then add 2100 to both sides and you divide by 44.25, making an estimate of 48 jackets to sell. To see her profit, you plug in 48 to her profits, "P (48)= 44.25(48)+2100". After her finishing, her profit is $24. | The most important facts, terms, and tips I need to remember from these three concepts are the terms from the business problems. Since there are many parts to it. | The part I understood the most from these two concepts is the linear model since I got the hang of it pretty quickly. | The part I am still confused about from these two concepts is the exact definition of extrapolate. I think I got the right idea about it but I'm not 100% sure since there wasn't an exact definition in the video. | sarahi.oleal@hotmail.com | ||||

80 | 6/28/2013 22:53:47 | Leopo | Clara | First, you need to figure the ordered pairs. The ordered pairs are given in the story. The x-value represents the time and the y-value represents the amount of items sold. Then you must find the slope that is found by plugging in the ordered pairs into slope formula. Then you must finish solving the problem by answering the a, b, c questions. | To "extrapolate" data from the equation means to write in order to predict the future. For instance, in problem 3, it is asking you to predict,"extrapolate," how many sea shells she will sell during week 21 if the pattern continues. | Maddie loves purses so much that she decided to start a business selling purses. During the first week of selling, she had sold 12 purses. By the 6th week, she had sold 45 purses. Assuming her sales will follow a linear model, a) write the linear equation to model the number of her sales; b) calculate how many purses she will sell during week 3; and predict how much she will sell at week 21 if this continues. | First, I plugged in the "first week" as my x-value, 1, and y-value 12 because that's how much purses were sold in one week. Then I plugged in the number 6 as the sixth week and plugged in the number 45 as the amount of purses sold in the y-value. [(1,12), (6,45).] Then, I plugged in the ordered pairs into the slope formula: m= 45-12/6-1= 33/5. The slope is 7 (I simplified 33/5 to 7). To find the answer of a, I had plug in my numbers to y=mx=b form and find b. b equals 5 after I subtracted 7 in both sides. My answer was f(x)= 7x+5. For the problem b, I plugged in the "third week" into f(3) as well 7(3) and added five and received 26 as my answer. For problem c, I plugged in the number 21 into f(21), then added five, that equaled to 152. | The different types of costs we have is cost, revenue, profit and break-even point. The "cost" is the fixed costs and variable costs added together. Fixed costs are what it is paid monthly and "variable costs" is how much costs to make each item. "Revenue" is how much you charge for each item you sell. The equation for "revenue" is R(x)=__(x). "Profit" is what takes your revenues and subtracts your costs. The equation used is P(x)=R9x) - C(x). "Break- even point" is the point at which a business makes no money and also loses no money. An equation used is P(x)-0. | The difference between revenue and profit that revenue is how much you charge for each item you sell and profit is what you take your revenues and subtract your costs. For example, if I were to sell chips for a dollar, that would be my revenue because that is how much I am selling the chips. Now say that I was selling 30 chips that costs 10 dollars at the store. So, that means that I will have 30 dollars at the end of the day, but I would have made 20 dollars in profit. | Sally needed to make money so she can buy a new dress for her friend's birthday party. She went online and found the perfect dress for 50 dollars. She decided to sell hotdogs after her brother's baseball game. Her hotdogs cost 2 dollars each including a drink. This is the revenue. So Sally went to the store and bought all her ingredients needed to sell and the total was 20 dollars. After the fun, cool sale of selling hotdogs Sally counted the money in her room. She had made 70 dollars. Boy they were hungry! Sally then calculated the amount used to buy her ingredients and found out her profit to be 50 dollars. She was able to buy her dress, YAY! (Her mother decided to give her tax money, after Sally washed the dishes.) | First, you need to figure out the costs by using the formula,c(x), then find what you make, the revenue-R(x)=(x) and plug in to find the profit, then find the break-even point adding/subtracting and dividing to find its break even point, P(x)=0. | The important facts, terms and tips I need to remember from these three concepts are how cost, revenue profit and break-even point helps figure out the money you make in a business, books you read in a week, etc. | The part I understood the most from these concepts how to write linear models and evaluate word problems and master them. | nothing, i understand. | clara.leopo@yahoo.com | ||||

81 | 6/28/2013 23:13:11 | Leopo | Mary | First you need to find the two sets of ordered pairs. The x-value represents time and the y-value represents an amount. You then need to come up with a linear equation. You plug your two sets of ordered pairs into the rise over run formula. after that you use the y=mx+b to solve for b. then you have your formula. | Extropolate means to predict and when the plotting the points on a graph we assume that it creates a linear model. An example could be, that Susanna sells two potatoes in one week and on the third week she sells 20 potatoes. When we set these two points on a graph we assume that the line is linear. | Jesse has a weird obsession with cars. His girlfriend Mary thinks he has too many so she starts selling his cars. In the first week she sells 5 cars. In the ninth week she sells 29 cars. Assuming that her sales follow a linear model a) Write a linear equation to model her total car sales; b) calculate how many cars Mary will have sold by fourth week; c) predict how many total cars Mary will have sold by the 23rd week if the pattern continues. | First you find the two sets of ordered pairs. The x-value represents time and the y-values represent amount. In that case we have the ordered pairs (1,5) &(9,29). To make a linear equation you must take your ordered pairs and plug them in the (y2-y1)/(x2-x1). ex. (29-5)/(9-1)=24/8= 3 The slope is 3 so you plug it in y=mx+b with a ordered pair ex. 5=3(1)+b b= 2 So your linear equation is f(x)=3x+2 and that is your answer for a. For problem b, you plug it in f(4)= 3(4)+2= 14 So she will have sold 14 cars in the 4th week. For problem c, you do the same and plug in f(23)= 3(23)+2= 71 So she will have sold 71 cars by 52 weeks. | There is the fixed costs which the costs that business would pay monthly and it stays the same such as rent and advertisements. the other type of cost is variable costs and this is how much it cost to make each product. This cost depends on how many items you decide to make. | Revenue is how much a charge for an item like for instance you charge 10 bucks for each shirt you sell. Profit is the how many shirts you sold minus your costs. For example, if the monthly costs is 1400 and you charge 10 bucks for each shirt you sell and takes 5 bucks to make your item then you will use this formula P=R-C . you will then find your profit. | Mary is starting a business where she sells guitars. It costs 1300 for monthly equipment and rental fees, and $15 to make a guitar. She sells the guitars for $40 each. Write a (a) Cost Function; (b) Revenue Function; (c) Profit Function; and (d) estimate the number of pencils you will have to sell in order to break even( round up to the nearest guitar if necessary and find the amount of profit if you do round up.) | First find the cost using the equation C(x)= fixed costs+(variable costs)(x) ex. C(x)= $1300+ 15x Then you find the Revenue which is the how much Mary charges for the guitar. Using this formula, R(x)=___(x) ex. R(x)= 40x Next is the finding the Profit function. you use this formula to find the profit. P(x)=R(x)-C(x) (You use plug in the costs and the revenue) Ex. P(x)= 40x-(1300+15x) you must distribute the negative. 25x-1300 For d you must find if you Break the Even Point ex. 25x-1300=0 you need 52 guitars to meet the BEP to check you must Plug the 52 into the Profit equation ex. 25(52)-1300=0 so Mary just met the BEP | x-value = time y-value= amount extrapolate Fixed costs+ (variable costs)(x) R(x)=____(x) P(x)= R(x)-C(x) BEP P(x)=0 | Everything | Nothing | mary.leopo@yahoo.com | ||||

82 | 6/27/2013 18:35:15 | Lomeli | Ivan | To solve a linear model, you first read the problem and jot down any important numbers in coordinate form. The coordinate form should be set up as (time, amount). After setting that up, you use them to find the "slope" of the linear model, which represents the pattern. Then, you solve for b using any of the coordinates you first obtained. After b is found, you set up the mx+b=y equation. You use that equation to find what the problem asks you to find and extrapolate to find "future" results. | Extrapolating means to elongate, or extend in a sense, by using previously found "patterns". For example. you can extrapolate the amount of new students coming into a university by observing the amount of new students who came in last year. | Jeff is an all-time nerd who is obsessed with pokemon. Jeff decides to use his obsession to make others happy since his room is over-filling with pokemon stuff and he knows everyone loves pokemon secretly. Jeff decides to sell pokemon plushies to people around the school. During week 1, Jeff is able to sell 6 plushies since every high-schooler was afraid to admit they loved pokemon. However, as more and more nerds come out of the shadows, Jeff is able to sell 41 week 6 as more and more people begged him to collect more pokemon. Using Jeff's situation, assume his collection continues and dispersion flows nicely to follow a linear model. Write the linear equation to model his distribution of pokemon. Calculate how much he gave away by week 4. Also, predict how much stuff will have been given away by week 30 if his pattern continues. | First, you take any important numbers that were thrown at you and organize them into (time, amount) coordinates. You should have gotten (1,6) which were the numbers of plushies (6) sold week 1; and (6,36), which is the number of plushies (41) sold week 6. Then find slope using the two coordinates, you should get 7. Use any of the coordinates to find compose a linear model (i.e: y=mx+b using (1,6). 6=7(1)+b ----> b=-1) That is the linear model and you use it by plugging in what the problem asks to find the rest of the questions. Jeff should have given away 27 by week 4 and he should be giving away 219 by the 30th week of his freshman year. Good job Jeff. | We have two types of costs, Fixed costs and variable costs. Fixed costs are paid in a timely basis and stay the same amount all the time. Variable costs is how much it takes to make an item, and this should be a constant as the same item is being made. For example, a monthly phone bill that always costs $50.00 is a fixed cost. However, buying apps at $3 per app would be a variable cost. | Revenue is the price tag that is placed on the item, it is what goes into the business, the charge of what you're selling, such as the revenue you obtain from selling an iPod if you're the Apple Co. On the other hand, profit is what you get in the end after cost and revenue is taken into account. This means, what you earn after you subtract costs from your revenue. If the number resulting in profit is zero, then you just made ends meet. If it exceeds it, you're making business. In a BEP situation, the profit could be relatively small. For example, the Apple company is making large sums of profit, because their money at the end exceeds ends meet. | Jeff's giving away of pokemon plushies needs to stop, he is going broke and wants to make some profit to pay for college, so he decides to start SELLING his pokemon plushies instead of collecting them and giving them away. He begins his pokemon plushie business and opens a store. The store's maintenance costs 1500 a month for rental fees and bills; and each pokemon plushie he has to buy costs $2.00. Jeff sells them for $5.00. Write a cost function, a revenue function, a profit function, and estimate the number of plushies Jeff has to sell in order to break even and hopefull make a profit to keep everyone happy. | First, you obtain the cost function by looking at his fixed costs and variable costs, which should look something like this c(x)= 1500+2x (monthly costs plus price per plushie). Revenue function can be obtained by the price he places on the plushies, which should look like R(x)=5x. The profit function originally looks like this P(x)=5x-(1500+2x), and after simplifying it you obtain 3x-1500. You equal that to zero and obtain 500, which means Jeff has to sell 500 to make ends meet. | The relationship between (time, amount) coordinates and the differences between cost, revenue, profit, and BEP. More expecifically, BEP because it is important to remember that it has to be rounded up since merchandize can't be sold at a decimal. | That patterns in time and amount do exist and correlate with each other. Also, that when profit is zero, one is merely keeping a business alive and no money is being made. | How made profit can be represented in an algebraic equation. Also, how accurate extrapolated linear equations are. | ivan.lomeli@ymail.com | ||||

83 | 6/25/2013 16:19:22 | Lopez | Eriq | The first step is you have to identify the x vaule (time) and the y value (amount). After you find the two times and two amounts you put them into an ordered pair. After that you have to solve for the slope so you use the slope formula. Then you plug in one of the ordered pairs and the slope into y=mx+b. That will give you the y-intercept of the equation and now you have the full equation with the slope and y-intercept. Then you plug what every number into the formula to get the infomation needed. | The word extrapolating means to extend an unknown thing to find out a situation. An example would knowing how many toys are sold one weeks and estimating how many toys would be sold in 10 weeks. | Khloe loves making toys. During the first week Khloe sold 2 toys to her friends. During week 5 she had sold 22 because her toys became very popular. Assuming her sales follow a linear model, (a) write the linear equation; (b) calculate how many toys Khloe sold during week 3; and (c) predict how many toys she will sell durng week 20 if this pattern continues. | the first thing you have to do is find the two points. The first pair would be (1,2) becuase she sold 2 toys during the first week and remember x is the time and y is the amount. The second pair would be (5,22) because she sold 22 toys in the 5th week. Then you plug that into the slope formula which is y2 -y1 over x2-x1. This would give you a slope of 5. Then you can choose any pair and the slope to plug into the y=mx+b. I will choose (1,2) and the equation will be y=5x-2. Then for letter b you plug in 3 into your equation which will give you 13 toys for the third week. Lastly for letter c you plug in 20 and that will give you 98 for the 20th week. | There are two types of costs. One is the fixed costs and the other is the variable cost. The fixed costs is something you pay monthy and stays the same each month you pay it. The variable costs is how much it costs to make something. It varies on the type of item you make and how much you decide to sell. They are similar by the equation fixed costs + (variable costs)(x). | The difference between the revenue and the profti is that revenue is how much you charge for each item you sell and the profit is the amount after you subtract your revenue from the costs. An example is like if you sell 10$ for a toy that would be your revenue. The profit would be if the toy costs 5$ to make you would subtract that amount from your revenue. Then your profit would be 5$ so you will be making money. | Khloe is starting her toy business. it costs her $1000 for monthy equipment and rental fees and $2.00 for supplies for each toy. She sells them for $10 each. Write your (a) cost function; (b) revenue function; (c)profit function; and (d) estimiate the number of toys she will have to sell in order to break even. | First we have to find Khloe's costs. Her Fixed cost is $1000 and her variable cost is $2.00. That means that her c(x)= 1000+2x. Then we find the revenue, so we take how much she is selling each toy R(x)=10x. After we find the profti so we take the revenue and subtract our costs to get p(x)=8x-1000. Now we find the break even point so we set the profit equal to zero. That means she will need to sell 125 toys in order to not loose any money and not make any money. | extrapolate-to extend the thing we are looking for. the two different types of costs: Fixed-paid monthy and variable- how much it costs to make something. Revenue- how much you charge for each item you sell profit- take your revenues and subtract your costs BEP- the point at which you make no money and loose no money. | The part i understood the most was writing linear models and evaluating for world problems. It was very easy for me. | is the part about the break-even point when you have to round it. I do not understood why you have to plug back in the BEP to get a really small number. | shortylopez_12@yahoo.com | ||||

84 | 6/27/2013 20:35:17 | Lopez | Krystal | The first thing you have to do is find the slope by subtracting and dividing. Once you find your equation you plug in the amount to figure out how many things they did. You calculate and predict the other weeks. | Extrapolating is when you make the line longer. You need to do this to find out how much it is past a certain point. | Julian is collecting toy cars. By the first week he had 3 cars. On week 11 he had 83 cars. Assume he follows a linear model a) Write a linear equation b) Calculate the amount of cars he would have by week 4 c) predict how many he would have by week 22. | First you find the linear equation which is y=8x-5. You get this by finding the slope and the intercept. Now you calculate the amount for week 4 by plugging 4 into the x of the linear equation and get 27 cars. Now to predict for week 22 you plug that in, after you get 171 cars. | The first cost is the fixed cost which is when you pay monthly like 3000. The other kind of cost is a variable cost, this depends on how much of something you order so it may not be the same every month. You do not have to order the same amount of something every month. | Revenue s how much you sell something like Julian sells his car for $12. A Profit is what you have left after. For profit you have to take the revenue and subtract the costs. | Julian is starting a toy car business. It costs him $3000 for equipment and rental fees and $3 for supplies needed for the cars. Julian sells each toy car for $12. a)cost function b) revenue function c) profit function and d) estimate the number of cars he will need to sell to reach his break-even point. | To find the cost you need to add the fixed cost and the number of variable costs: C(x)=3000+3x. The revenue is what you sell the item for: R(x)=12x. For the profit function you need to revenue minus the cost; you distribute and if you get a decimal you will need to round it up and that is your bep. | Cost, Revenue, Profit, and Break-even point. You have to know what each mean and the difference between them. | i understood the cost of something the most. | I am still confused on the profit and break-even point. | krystal.lopez77@yahoo.com | ||||

85 | 6/28/2013 22:29:59 | Lopez | Mateo | To start off i had to find what she started with her first week. then i found what she did on her 5th week. And then I had to find the slope using the two points I got from that. | what this means is to guess what is going to keep going off after the points you have. like if you sell 6 cups in 1 week and by the 5 week you sell 46 find how many you sell by the 25 week. | Bob is a coin collector. He collects any type of coin he finds that are different or unique. His first week he found six coins. By the end of his sixth week of collecting he had found 66 coins. | To start off i had to find what she started with her first week, which was (1,4). Then i found what she did on her sixth week, which was (6,34). And then I had to find the slope using the two points I had. i got m=6. i then plugged it into F(3)=6(3)-2 and my result was 16. For C i used F(21) and got 124 as my result. | Both: deal with money. are the cost of something. Fixed: the amount you pay monthly Variable: is how much the product cost to make | revenue is how much your charging for the product and profit is the money your making. | As soon as Bob reached his goal in his collection he opened his own antique shop. it costed him $1400 for monthly equipment and rental fees. And $.55 for supplies and cleaning the coins. he sold each coin for $6.50 | to start i had to read the problem and then find the Fixed costs, Variable costs, and the Revenue. once i did that i solved for a) which was c (x)=1400+.25x. then for B) r (x)=.75x. Then i did C) P(x)=.75x-(1400+.25x). And lastly D) P(x)=.5x-1400=0 so i had to solve for x. | all the business terms and equations. | The first part with the linear models. | i was a little confused on the business running one because of all the different equations but its all good i have it down now. | lopez.mateo15@yahoo.com | ||||

86 | 6/27/2013 19:08:45 | Luong | Angela | First set up two sets of ordered pairs. After discovering the ordered pairs, find the slope using (y2-y1)/x2-x1)=m. Then use y=mx+b, plug in the slope that you found and use one of the ordered pairs that you created. One you have found b, you now have the slope and b to plug into y=mx+b, that will be your linear model. To find the value of a function, plug in the function into the linear model that you had created. | Meaning to extending the line model (assuming it is a linear model) to guess to see what is happening past the plotted points that you have on the graph. | Amber likes to create bookmarks as a hobby. In week 1, she creates 5 bookmarks. During week 6, she has more time to herself and creates 12 bookmarks. Assuming her completion of bookmarks follow a linear model, a) write a linear equation to model her completion of bookmarks; b) calculate how many bookmarks she completed in week 3; and c) predict how many she will make in week 24 if this pattern continues. | So first, I had followed the previous examples by finding the information for the ordered pairs. I ended up with (1,4) and (6, 34); the x being time (# of weeks she sold seashells) and y being the number of seashells she had sold that week. From there I used (y2-y1)/x2-x1)=m to find the slope, I had gotten 6 as an answer. I then used y=mx+b, plugging in the 6 and using the smaller ordered pair (1,4) in the equation. I had gotten -2 as my b. The linear model is then f(x)=6x-2; this is all for part a. For part b, I had plugged in the number 3 in the equation: f(3)=6(3)-2. The answer was then 16 seashells; this is part b. Finally for part c, I also just plugged in the number 21 that was given in the problem, repeat steps in part b. The answer I had gotten was 124 seashells for week 21. | The two types of cost is fixed and variable. Fixed cost is a number that does not change, like monthly rent, the pay remains the same every month you pay it. For variable cost, the number changes and varies like if you are selling ice cream, you sell more during the summer than you do during the winter or variable is also the number of ice cream cones you sell every day, you can sell more one day than you did the other. | Revenue is the money you make, how much each item you sell is charged. Profit is the money that is left after you have paid the bills, meaning it is the remaining amount after you subtract bills like advertisement (it is basically the revenue minus the cost). It is like the ice cream business, your revenue is $350. After you have subtracted the cost of bills, which is possibly $150, then the profit would be $200. | Amber decides to sell her bookmarks. It costs $1200 for monthly equipment and rental fees. It cost .50 cents for supplies for each bookmark. Amber sells each bookmark for a dollar. Write the a) cost function; b) revenue function; c) profit function; and d) estimate the break even (round up if necessary). | Cost is the money for monthly rent and the supplies so: C(X) = $1200 + .50x. Revenue is basically the amount of money you are selling the item for: R(X) = 1x and Profit is the remaining money after you have subtracted the cost from the revenue: P(X) = 1x - (1200 + .50x). Remember to distribute the negative to everything in the parenthesis and combine like terms: .50x-1200. For the break even, add the 1200 to the other side so it looks like this: .50x = 1200, then divide by .50x; which is 2400 bookmarks, this is the amount for the break even. | For concept 6, I need to remember that x will be the time and y will be the amount and understand what extrapolating means. For concept 7, I need to make sure for myself that I do not mix up the number for cost and revenue. I also need to remember to distribute the negative in P(x) so I get the correct answer. | I understand mostly everything because it is familiar to me from College Algebra. I understand writing linear models and finding cost, revenue, profit and break even. | I get a bit confused about finding profit, but after rewatching the video, I understand it better now. | angelaluong90@yahoo.com | ||||

87 | 6/28/2013 16:13:23 | luong | david | First, you have to find the ordered pairs where x is represents time and y represents amount. Once you have two ordered pairs you can find the slope by using the formula. After you have found the slope plug the slope into either the slope-intercept formula or the point -slope formula. Finally when you have the equation you can plug in any x value to find the y. | Extrapolate means to extend the line past a point you already know to assume an answer by following a pattern. In a way it is like extending the graph past what you know based on a pattern you see. | Steve loves playing video games. The first week he played 28 hours of video games. The sixth week he played 168 hours of video games. How many hours did he play on the third week? | Steve played video games for 28 hours on the 1st week and he played 168 on the 6th week. You make those into ordered pairs by taking the time and the amount. So you get (1,28) and (6,168) you find the slope by using the slope formula. The slope ends up being 28. Then you plug that into either the slope-intercept or point-slope form and solve for the y intercept. The y-intercept is 22 then you plug everything in to the equation to find the third week which ends up being 62. | We have two different cost: a fixed cost and a variable cost. Fixed cost differs from variable cost because fixed costs remain constant and doesn't change. Variable cost, on the other hand, vary from day to day or month to month never being the same. | Revenue is how much you sell the item for, while profit is how much you make after all the cost have been cut from your revenue. For example if you sell an item for 5 dollars (that's your revenue) but it cost 2 dollars to make (that's your cost) then you profit 3 dollars. | Steve is opening a pet store. it cost him $1400 for monthly equipment and 10 dollars to take care of them, and he sells pets for 20 dollars each. How many pets will he need to sell to break even? | First we find the cost: c(x)= 1400 + 10x Then we have to fine the revenue: R(x) = 20x Then we fine the profit: P(x) = 20x - (1400 + 10x) After solving that you would even up having to sell 140 pets to break even | The most important concepts are the key terms and equations or cost, revenue, profit and BEP. | I understood this whole chapter fairly easily. | nothing | luong_david@sbcglobal.net | ||||

88 | 6/24/2013 11:38:30 | Luong | Sidney | Basically, you dissect the word problem. Knowing that the x value represents time and y value represents amount, you can already pull out corresponding pieces of information. Once you find your ordered pair, you use the slope formula to find out the slope. From there you plug it into the slope intercept form so you can have an equation that represents the pattern. Next you have to plug in a ordered pair so you can find the y-intercept. Now that you have an equation, you can solve questions that involving how many items are sold a certain time by plugging in number for the x. | Extrapolate means to expanded farther knowing that it follows a linear model, meaning that it follows the same pattern. For example, lets say that in the first week of school Tom read 2 books and assuming she follows a linear model, by the 5th week of school, Tom read 9 books. Predict how many books Tom would have read by week 52. Knowing the pattern from the first week to the 5th week, we assume that this pattern would continue all the way to week 52 so that we can solve the problem. | Sidney loves to watch Korean dramas. In the first month, Sidney watched 5 dramas. By the 4th month, she watched 20 dramas. Assuming she followed a linear model, write the linear equation to model how many dramas she watched, calculate how many dramas Sidney would have watched by the 5th month, and predict how many total dramas Sidney would have watched in 12 months. | Remember that the x- value represents time and the y value represents an amount. Knowing that information, in the FIRST month Sidney watched 5 dramas. You can put this piece of information into a ordered pair, (1,5). How did I get that? Well the 1 represents the first month and time is shown by the x value. The 5 represents how many dramas Sidney watched so it shows the amount, y value. The next ordered pair would come from the "4th month she watched 20 dramas," (4, 20). The first part of the question asks you to write the linear equation. So using the slope formula you find that the slope, m, is 5. Then you use the slope y intercept form and plug in a ordered pair to find out b. In this case your linear equation is y= 5x. For the second part it asks you to calculate for the 5th month. All you have to do is plug in the 5 for x and solve. y= 5(5) so y= 25 dramas by 5 months. Finally the last part tells you to predict how many dramas Sidney watched in 12 months. Once again you plug in 12 for x and solve. y=5(12) so y= 60 dramas by 12 months. | Cost is divided into two parts, fixed costs and variable costs. Fixed costs are the amounts paid monthly and stays the same every month. Variable costs are the amounts determined by how much it costs to make each item. Variable costs usually vary monthly based on how many items you decide to produce. | Revenue is how much you charge for each item you sell. Profit is the amount you get after subtracting your costs from your revenue. For example I sell shirts that cost $5. Lets say I sell 20 shirts meaning my revenue is 100 dollars. However it costs me 20 dollars for both my monthly equipment and supplies for each shirt. I make $80 overall because I have to subtract the 20 dollars from the supplies and advertisements I used. That 80 dollars is your profit. | Sidney decides she needs some money to buy all the Korean dramas she likes and creates a business that sells posters of famous Korean celebrities. It costs her $1200 for monthly equipment and rental fees, and $1 for supplies for each poster. Sidney sells each poster for $4. Write Sidney's (a) Cost Function; (b) Revenue Function; (c) Profit Function; and (d) estimate te number of posters Sidney will have to sell in order to break even (round up to the nearest poster if necessary and find the amount of profit if you do round up. | Since C(x)= fixed costs + (variable costs)(x), C(x)= 1200+1x. Revenue is how much you charge for each item and Sidney charges each poster for $4, so your revenue is R(x)= 4x. To calculate profit means that you take your revenue and subtract your costs. In this case, take 4x and subtract 1200+1x -> P(x)= 4x- (1200+1x). Don't forget to distribute the - to 1200 + 1x. once you do that your P(x)= 3x-1200. The final part is to see how many posters Sidney has to sell to break even. To do this, take your P(x) and make it equal to 0. So once you solve 3x-1200= 0 then you find that Sidney needs to sell 400 posters to to break even. | the x value will ALWAYS represent time, the y value will ALWAYS represent an amount, the meaning of extrapolate, for business problems you must know what cost/revenue/profit/ break even point mean, cost is broken into two parts- fixed costs and variable costs, (x) is the number of items, BEP should be rounded up to the nearest whole until even if it is illogical | writing linear models and evaluating for word problems | differentiating the profit and revenue amounts. | cubesity@hotmail.com | ||||

89 | 6/23/2013 11:23:06 | Mai | Nga | The first step in solving a linear model word problem is to determine the two sets of ordered pairs. The x-value will represent the time while the y-value represents the amount. After determining the two ordered pairs, use the slope formula to formulate the linear equation. Afterwards, use plug in the values to solve for the answer algebraically. | The word extrapolating means to estimate a value based on extending what is known. If the following data is linear, and you are given (1,2), (2,3),(3,4), you can assume the following point will be (4.5) because you extended the line. | Nicole has finally discovered her passion for eating pies. During the first week, she ate 5 pies. During the 8 week, Nicole consumed 54 pies. Assuming her consumption of pies follow a linear model, (a) write the linear equation to model her eating habits; (b) calculate how many pies did she eat in total by week 4; (c) predict how much she will eat in total by the 13 week if this pattern continues. | The first step to solve (a) is to set up two sets of ordered pairs. The week number determines the x value and the amount determines the y value. This can now be expressed as (1, 5), (8,54). The next step is to find the slope. To find the slope, subtract (y2 by y1) and divide that by (x2-x1). Afterwards, plug the slope and a point into the slope intercept. This can now be seen as (5)=7(1)+b. To solve for b, subtract 7 from both sides, to find that b=-2. The linear equation is y=7x-2. To solve for (b), plug the week number, 4, into the x-value. Then solve the equation, f(4)=7(4)-2, by multiply 7 with 4 to get 28, and then subtracting 2,to get 26. 26 pies is how much Nicole would have eaten by week 4. To solve for (c), plug 13 into the x-value. The equation will be f(13)=7(13)-2. Multiply 7 with 13 to get 91,subtract 2 and get 89. By the 13 week, Nicole would have eaten 89 pies. | the two different types of costs are fixed costs and variable costs. They are different in the way that fixed costs are paid monthly and remains consistent, while variable costs is how much it costs to make each time, It can vary monthly. While these two are different, they are similar in the way that they both fall under costs and deal with money. | Revenue is how much is charged for each item, while profit is the amount you gain after you subtract your costs. Revenue can be that you charge customers 10 dollars for a book. Profit is when your expenses were five dollars. To find the profit, you subtract the revenue, 10, by the costs, 5, which gives you the profit of 5 dollars. | Not only does Nicole eat pies, but she also sells them too! It costs her 1200 dollars in monthly fees , and 3 dollars for the supplies. She sells each pie for 10 dollars. Write your (a) cost function; (b) revenue function; (c) profit function; and (d) estimate how much Nicole will have to sell in order to break even (round up if necessary). | (a) The profit function is C(x)=fixed costs =variable costs(x). Plug in the number to get C(x)=1200+3(x). (b) The revenue function is R(x)=__x). Nicole charges 10 dollars so you plug that in to get R(x)=10(x). (c) To find the profit function it is R(x)-C(x). Plug in the revenue and costs to get P(x)=10x-(1200+3x). Distribute the - to get 10x-1200-3x. Simplify to get P(x)=7x-1200. To find the BEP, set the equation to 0 and add 1200 to both sides, then divide by 7 to get 171.4, round up to 172 pies. To find the amount of profit made, plug in 172 into P(x)=7x-1200. Solve it to get a 4 dollar profit. | The most important things that I should remember is the steps to solve linear models and word problems. I should also be able to recall cost, revenue, profit and BEP. | The part I understood the most was the linear models. | I understood the two concepts. | maikngaledge@yahoo.com | ||||

90 | 8/12/2013 14:25:31 | Manalo | Catherine | First step is to find the order pair in the word problem. Then you find the slope between the order pairs, and plug it into a slope intercept equation. Plug in an order pair, and solve for b. Then use the final equation to solve the word problem. | Extrapolating means to assume that the line will continue how it is going. So if Line A is going upward, we are going to extrapolate (ASSUME) that it continues its direction and hope it doesn't take a dive. | Iona has a passion for taking pictures. So she began taking pictures of her friends modeling their back to school fall wardrobe. In her first week she took 6 pictures of her friends. By week 3 she has captured a total 26 pictures. Assuming her progress follows a linear model, (a) Write the linear equation to model her photos; (b)calculate how many photos Iona has taken by week 7; and (c) predict how many photos she will have during week 32 if this pattern continues. | First problem, (a), you are to find the equation of the word problem. First you translate the word problem into two coordinates, (1,6) and (3,26). Then you find the slope (m) by subtracting y2-y1/x2-x1; 26-6/3-1= 10. Next step is to find the b of the equation. so you plug in an ordered pair (1,6) and slove for b. the answer is -4. So (a) is y=10(x)-4. (b) Finding how much pictures Iona has taken by week 7, is just plugging x, 7, into the equation. y=10(7)-4. The answer is 66 photos. (c) Predict how many photos she will have taken by week 32. You simply plug in x, 32, to the equation. y=10(32)-4, The answer is 316. | There are two different types of costs; fixed costs and variable costs. Fixed costs are determined and official price of stuff like rent. Variable costs is the cost of how much money is spent needed to make something. Fixed costs stay the same, while variable costs can change. | Revenue is how much you bring in, while profit is how much money you earn after the bills are paid. For example you are selling brownies. A box of brownie mix cost 4 dollars and make a batch of 12 brownies. you sell each brownie for 50 cents. once you have sold all 12 brownies you have made 6 dollars. Your revenue is how much money you bring in, which is 6 dollars. but your profit is how much you make after your costs are paid. it took 4 dollars to buy the batch, and you brought in 6 dollars. Once you have paid the cost of batch, 4, your profit is 2 dollars. | Iona begins to make copies of her photos and sell them. Renting out the equipment cost 30 dollars a month and each photo copy costs 10 cents. She begins selling the photos for a dollar. Write the (a) cost function, (b) revenue function, (c) profit function, (d) and estimate the the number of photos she will need to sell in order to break even. | (a)To find the cost function, you add the fixed costs with the variable costs. 30+.10(x) (b)then you find the revenue function by multiplying how much you charge for an item, by the number of items sold. Rx=1(x) (c)Finding the Profit function taking your revenues and subtracting your costs. so 1(x)-(30+.10(x)) simplify and you get P(x)=30+.9(x) (d) to solve how much you need to sell to break even you need to set the profit function and equal it to zero. 30+.9(x)=0 You need to sell at least 34 photos to break even. | The most important terms from these three concepts are fixed costs, variable costs, revenue, and profit. Not only their terms, but the equation each term has. | The part I understood the most from these two concepts is the difference between revenue and profit. | The part i am still confused is the extrapolating from an equation. | catmanalo96@gmail.com | ||||

91 | 8/14/2013 9:21:35 | Mankin | Emmanuel | First, you find the rate of change using the two sets of ordered pairs that are given. Next, you choose an ordered pair (preferably the one with smaller numbers) and you plug those numbers into the slope-intercept formula of y=mx+b and plug in the rate of change you just found where m is in the formula. Then, you solve for b. Once you get your formula (ex: f(x)=6x-5) then you plug in the number that represents time, such as 5 days, into where x goes in the formula. You repeat the least step until all of the numbers that are supposed to replace x are used. | Extrapolating means to predict using past data or knowledge. So, if i want to figure out how many students will be coming into school next year, I could predict the number by looking at how many students left the previous year. | Josiah has a part time job at Starbucks. When he first started working there he made a total of 35 drinks in the first week. After the 12th week there he made a total of 255 drinks. Assuming his drink making follows a linear model, (a) Write the linear equation to model his total drinks made; (b) calculate how many drinks Josiah will have made by the 3rd week; and (c) predict how many drinks he will have made by the 56th week, a year and a month after his first day, if this pattern continues. | First, find the x-values for the given weeks in the problem and then make two sets of ordered pairs using the given number of drinks that he made by the end of the two given weeks. Next, you find the rate of change using the two ordered pairs using the formula m= (y2-y1)/(x2-x1), which would be m=255-35/12-1= 220/11=20. After you have found the rate of change, you can now solve for b using the slope-intercept formula. Choose an ordered pair to plug into the formula and plug in the numbers to the appropriate variable, which would be 35=20(1)+b. Multiply 1 by 20, which equals 20 and subtract 20 from both sides so b=15. Now you have your formula, which is f(x)=20x+15. to solve for the 3rd week, you plug in 3 where x should be and then evaluate to get f(3)=20(3)+15= 60+15= 75. To solve for the 56th week, you repeat the last steps to get: f(56)=20(56)+15= 1120+15= 1135. | A fixed cost is a rate that never, or rarely, changes. While a variable cost varies on how much it costs to make an item, so if it was $2 to make a pencil and I had to make 100 pencils that month, then it would cost me $200 that month to produce that number of pencils, while the next month if I only had to make 20 pencils then it would only cost me $40 to produce the number of pencils that month. | Revenue is how much you charge consumers for your item being sold. So, if I was selling homemade doughnuts for $2.50 each, then that would be my revenue. Profit is how much you make from selling your product after subtracting your costs from how much you made from your revenue. If it only cost me $1 to make a doughnut, and I made 100, then my costs would be $100. And if I sold all of my doughnuts for the given price then my profit would be $150. | Josiah started his own coffee business. It costs him a total of $1200 for monthly equipment and rental fees, and $1.50 for supplies to make coffee drinks. He sells each drink for $3.50. Write your (a) Cost Function; (b) Revenue Function; (c) Profit Function; and (d) estimate the number of drinks Josiah has to sell in order to break even (round up to the nearest drink if necessary and find the amount of profit if you do round up). | write the cost function: C(x)=1200+1.50x write the revenue function: R(x)=3.50x write the profit function: P(x)=3.50x-(1200+1.50x) or 2x-1200 After you have simplified the profit function, you equal the equation to 0 and solve for x by adding 1200 to both sides then dividing 2 on both sides to get 600. (2x-1200=0 ... 2x=1200 ... x=600) | I need to know what the x-values and y-values stand for in a linear model, the two types of costs, what revenue is, what profit is, and what a break-even point is. | I understood both of the two concepts, but I do feel like I understood the Cost, Profit, Revenue word problems. | I am not confused about anything in these two concepts | emmanuel.mankin96@gmail.com | ||||

92 | 8/22/2013 14:43:26 | Marroquin | Iris | First, you set up an ordered pair with the given information in the problem.Then, you find the slope using the slope formula. Then you plug in the slope into the y=mx+b formula to find the y-intercept. Once you have your equation, you replace the y with f(x)and plug in whatever week your trying to calculate and repeat the same process. | It means predicting how many it will be in a longer period of time, as long as it follows a linear model. If you know someone gets 5 things in 1 week, you will be able to predict how many they will have in 14 weeks. | Sara wants to read as many books as she can before summer ends. In the first week, she reads 2 books. In the fourth week, she reads 11. If she follows a linear equation, how many books did she read in the third week, and how many books will she read in 12 weeks. | First, we take out an ordered pair from the information given, which would be, (1,2),(4,11). Then we find the slope using the slope formula which will be 3. Then we plug it into the equation along with one of the ordered pairs, 2=3(1)+b, so b=-1; y=3x-1. To figure out the other weeks, you need to replace y with f(x), x being the number of weeks.Then you follow the same steps and in 3 weeks, Sara read 8 books. In the 12th week, she will have read 35 books. | There is the fixed cost and the variable cost. The fixed cost is a monthly paid cost that usually stays the same throughout every month. A variable cost is how much it costs to make something. The variable cost varies depending on how many items you either purchase or sell. | Revenue is what you make from the items that you sell; In other words, how much you sell your items for. Profit is the money you have left once you've paid all the costs, bills that needed to be paid in order to run your business. For example if your revenue for a t shirt is $10, but the cost to make each t shirt is $4, then your profit is $6. | Sara opened a bookstore. Monthly costs add up to $1200, and $7 for each book. She sells each book for $12 dollars.Write your Cost Function, Revenue Function, Profit Function and estimate number of books she will have to sell in order to break even. | First, you find the cost function which is the the variable cost subtracted by the fixed cost(x). Then you take out the revenue cost which is 12x. Then you find the profit cost which is the cost function subtracted from the revenue function; 12x-(1200-7x). Then you combine like terms. P(x)=19x-1200=0. Then you solve the equation. It equals 63.157 but you round up to 64. | The most important facts, terms, and tips I need to remember from these three concepts are the different equations i need to set up in order to get the correct answer. I also need to remember all the business vocabulary. | The part I understood the most from these two concepts is how differently you set up each one and how important it is that you do the steps right. | I'm somewhat confused on how you figure out the profit from the equation. | mar.iris88@gmail.com | ||||

93 | 7/5/2013 15:29:40 | Martinez | Edward | To solve a linear model word problem you first need to see how many items were sold on each week. Then you will plug them into the slope formula. Once you find the slope you will plug in the slope and an item and week as x and y into the slope-intercept form. Then you will have b. Now that you have the slope and b you can calculate how many items were sold on any given week. | Extrapolating means to look at patterns and estimate the next pattern. In weather forecasts, they look at weather patterns and extrapolate future weather patterns. | John loves to play video games for fun. One day, he was in desperate need of money to buy the new Xbox and he saw his old video game collection collecting dust so he decided to start a used video game business. During week 1, he sells 4 video games. During week 6, because his low prices attracted more customers, he sells 34 video games. Assuming his sales follow a linear model, (a) Write the linear equation to model his sales; (b) calculate how many used video games John sold during week 3; and (c) predict how many used video games he will sell during week 21 if this pattern continues. | First thing I will need to do is find how many used video games were sold in week 1 and week 6 and then plug them into the slope formula. The slope is 6. I will plug the slope into the slope-intercept form and also plug in a week and how many used video games were sold as x and y. b=-2. If we plug that into the slope-intercept formula we get y=6x-2. Now we can find how many used video games were sold on week 3. Just plug in the 3 and subtract the 2 and the answer is 16 used video games. Same thing for week 21, just plug in the 21 and subtract the 2 and the answer is 124 used video games. | Both fixed costs and variable costs contribute to the cost a business pays every month. But fixed costs are the same every month. Variable costs are based on how many items are produced in that month. | Revenue is how much you are charging for each item you sell. And profit is how much money you make from those items minus the costs. It costs Barnes and Noble 50,000 in monthly fees and equipment and $5.00 for every book (just guessing). Then their revenue is going to be how much they charge for each book they sell. But their profit comes from how much revenue they get from the books minus the costs. | John is starting a used video game business. It costs him $5000 for monthly payments and rental fees, and $2.25 in refurbishing for each used video game. He sells each used video game for $10. Write your (a) Cost Function; (b) Revenue Function; (c) Profit Function; and (d) estimate the number of used video games he will have to sell in order to break even. (Round up to the nearest used video game if necessary and find the amount of profit if you do round up) | To find the cost function I will plug in the fixed cost and the variable cost.To get the revenue function I will plug in how much is charged for each video game.To get the profit function I will take the revenue and subtract the costs. I will distribute the minus sign so that the cost is negative and then I will combine like terms. To find how much he needs to sell in order to break even I will need to set the profit function equal to zero then solve. I got 645.16 but I need to round up so it is 646 used video games. To find the amount of profit I simply plug in the break-even point to the profit function and solve. John got a small profit of $6.50. | How to write linear models and solve them. Writing and solving cost, profit, and revenue word problems. Fixed cost is the same every month and variable cost varies. | Writing and solving cost, profit, and revenue problems. | I am not confused on these two concepts. | rmartinez57@sbcglobal.net | ||||

94 | 8/26/2013 15:37:57 | martinez | america | first find he equation for the cost, secondly find the revenue of your product, once you have found these two subtract the revenue from the equation of the cost this will give you the price, lastly find your break-even point by using your equation of the profit and equaling it to zero. | extend the application of (a method or conclusion, esp. one based on statistics) to an unknown situation by assuming that existing trends will continue or similar methods will be applicable. . Ex: knowing that sally in one week found 10 shells and in week 5 found 35 shells then using extrapolating by believing she followed her linear model to figure out how many shells she found in the 21 week. | Peter likes to collect pebbles. During week 1, he collected 10 pebbles. During week 7, he finds a whole bunch of pebbles by his house so he collects 37. Assuming his findings follow a linear model, (a) write the linear equation to model his pebble collection; (b) calculate how many pebbles Peter had in his collection during week 7; and (c) predict how many pebbles he will have during week 50 if this pattern continues. | first you write two separate points x being the week # and y being the # of pebbles. after use the equation m=y2-y1/x2-x1 your answer will be your slope; after finding your slope use y=mx+b to get your slope formula. Using your new slope formula plug in the week given in the word problems to find how many pebbles he collected each week. | the two types of costs are your fixed costs and your variables. Your fixed costs are your expenses you pay monthly such as light, water, etc. Your variable costs are how much it costs to make each item you sale. | Revenue is how much you sale your item for. Price is how much you make after you have payed off all your costs. Ex of revenue: at school chips are sold for $.50 each Ex: you make a lemonade stand and sale it for $.50 at the end of the day you make $10 but you have to give $5 to your mom to pay her for the lemons and sugar she payed for you to make the lemonade. | Peter is starting a decorated pebble business ( you get to decorate and personalize your own pebble.) It costs $1400 for monthly equipment and rental fees, and $.15 for supplies for each pebbles. He sell each pebble at $.75. Write your (a) cost function; (b) revenue function; (c) Profit function; (d) estimate the number of pebbles he will have to sell in order to break even (round up if needed to.) | First of write the equation for the cost which is the number of fixed costs plus variable cost. After this write down the price per item is (how much peter sells the item for.) Next, subtract the price per item from the equation of cost to find your profit. Finally, write your profit down and equal it to zero, solve the equation this will give you your Break even point. once you have found your break even point plug it in into your profit equation. | the equation for the cost, revenue, profit, break even point. Cost- c(x)=fixed cost + valuable cost Revenue- R(x)= how much the item cost Profit- P(x)= R(x)- C(x) B.E.P- profit=0 | the concept i understood the most was the linear models. | what i still dont quite get yet is how to find your mall profit after finding your B.E.P. | martinezamerica33@yahoo.com | ||||

95 | 6/28/2013 0:47:22 | Medina | Cecilia | To solve a linear model word problem you must first set up your two ordered pairs once you have your two sets of ordered pairs you use the formula (Y2- Y1)/ (X2-X1) to find the slope between those two points. once you have found the slope you plug in the the information you have into Y= Mx +B and you get your equation. | The word extrapolate means to use the information you are given to make a predication. | Becky likes making bracelets. In the first week she made 8 bracelets. By the 7 week she had made 32 bracelets. Assuming her bracelet making follows a linear model,(a) write the linear equation to her bracelet making,(b) calculate how many bracelets Becky made during the 3 week.(c) predict how many bracelets she will make in the 11 week. | The first thing to do in this problem is to set up your two ordered pairs from the problem which will be (1,8) and (7,32). to find the slope of these ordered pairs you must use the formula (Y2-Y1)/(Y2-Y1) after plugging in the numbers into the equation your slope is 4. Next you will chose one of your ordered pairs and your slope and plug it into the equation Y=Mx+B. After plugging them in your linear equation is y=4x+4 which is the answer to A. For question B it is asking for the amount of bracelts Becky made in the third week. To solve for the amount she made you will plug in 3 to the linear equation you got in question A which is f(3)=4(3)+4 is equal to 16 Becky made 16 bracelets in the thrd week. Lastly for question C they want you to predict the amount of bracelets she will have made in the 11th week. To do this you will plug in 11 into the linear equation which is f(11)=4(11)+4. The answer to this will be 48, Becky will have made 48 bracelets by the 11th week. | The two different types of cost we have are Fixed costs and Variable costs. A fixed cost is something you pay monthly like advertising and rent. While variable cost is the amounts it cost to make an item but the cost may not always be the same. The thing they both have in common is they both have to be paid monthly. | the difference between revenue and profit is revenue is the amount of money you charge and revenue is the money you make. for exampe you charge 20 dollars for jeans but you make 15 dollars because it costs 5 dollars to make them. | Becky is starting her bracelet selling business . It costs her 60$ for equipment and $1.50 for materials per bracelet. Becky sells each bracelet for $2. Write the (a) cost function (b) revenue function (c) profit function and (d) estimate the number of bracelets you will have to sell to break even. | The first thing to do in this problem is identify your items. $60 is your fixed cost, $1.50 is the variable cost, and your revenue is $2. Question A asks for the cost function which is C(x)=$60 +$1.50 quest B is asking the revenue function which is R(x)= 2x Question C is asking for the profit fuction and that formula is P(x)= R(x) - C(x). next you plug in you values into the equation which is (2x)- (60 +1.50x) after that you distribute the negative sign and combine like terms and get P(x)= .50x -60 For question D they are asking to estimate the number of bracelets Becky has to sell to break even. To do that you set the equation equal to zero and subtract 60 to the other side to get X by its self. once you have X by its self you divide by .5 on both side and get 120. Becky has to sell 120 bracelets to break even. | the most important terms to remember in these concepts are extrapolating, fixed cost, variable costs, revenue, profit, and break even point. | the part i understood the most was how to solve the linear models. | the part i am still sorta confuse on is how to find the break even point. | ceciliamedina1994@gmail.com | ||||

96 | 8/1/2013 16:17:35 | Melo | Daniel | Make sure you have ordered pairs. Then find m . Plug in the numbers so you end up with an equation. | it means to expand what you know following the pattern | Katherine likes to collect marbles. In the first week she had 5 marbles. By the end of he 6th week she had a total of 46 marbles. write a linear equation to model the numbers. b how much will she had found on the 3rd week. c predict how much she would have found in 10 weeks. | So step one is to make two ordered pairs. The first one will say (1,6) because on the first week she had 5 marbles. The other would be (6,46). then you will find m. you will use y2-y1/x2-x1 plug in the numbers and will equal 8. on the third week she would have collected 24 marbles. on the 10th week she would have collected 78 marbles | we have fixed cost which is the cost you pay monthly. The other is the variable cost which is the amount of money it cost to make a product | revenue is how much you charge and profit is how much you make. | katherine wants to start a business selling makeup. it cost 1000 a month to get all the makeup, it cost 2.00 to ship each box of make up. she sells the make up for 15. | a) c(x)= 1000+2x this is the first step for costs. b Then for revenue its r(x)=15 for how much she sells each makeup. c P(x)= 15-(1000+2) You distribute the negative sign so it should be 13-1000. Then equal it to 0 13-1000= 0 add 1000 to both sides and then divide 13. the answer should be 77 | cost, revenue, profit, break even, extrapolate | everything | nothing | daniel_melog@yahoo.com | ||||

97 | 8/26/2013 18:50:07 | Mendoza | Trisha | Cameron always wanted to start her own business. But the problem is she was only 10 years old and there was no way that could happen. Until she decides that maybe she can sell LEMONADE. So she built her stand and had cups of lemonade set. The first week was very slow and she only sold 15 cups of lemonade. But after week 5 it was becoming extremely hot so she was able to sell cups lemonade. Determine the linear equation, calculate how much she sold the 2nd week, and predict how much she will sell her 7th week. | Extrapolating means the same as evaluating and solving for the missing parts of it by plugging it in. | Cameron always wanted to start her own business. But the problem is she was only 10 years old and there was no way that could happen. Until she decides that maybe she can sell LEMONADE. So she built her stand and had cups of lemonade set. The first week was very slow and she only sold 15 cups of lemonade. But after week 5 it was becoming extremely hot so she was able to sell cups lemonade. Determine the linear equation, calculate how much she sold the 2nd week, and predict how much she will sell her 7th week. | The first step is to determine the weeks and match them with their amount sold. So the first week we can out (1[week], 15 [cups sold]) then we take the fifth week and write (5 [week], 45 [cups sold]). After wards we use rise over run in order to find our "slope". That gives us 30/4. We then divide that and get 7.5. After that we plug in what we know to y=mx+b in order to solve for b. after pluging I'm the slope and points then solving for b we get 7.5. Now were ready to plug in the weeks we need to know into x and solve the equation.In two weeks she sold 22.5 and the other happened to be 60 | The first cost there is, is fixed costs. This is basically the payments that come monthly like rents. There is also variable costs which is the price of every item made. These two are added together and the variable costs is always sided by the exponent x. Then there's revenue which is the amount that the item is being sold for or you are selling it for. This is represented with the r. Then there's profit which is the difference of the money spent and the money used. Break even is when you don't make not spend money this is always set to zero | Revenue is the amount you are selling and item for but profit is the amount made with the expenses that came with it. Lets say I buy a Tshirt for 15 dollars and I sell it for 20. 20 is my revenue because that is what I'm selling it for. But when I subtract it from how much I spent I get five as my profit which is the total I made in the long run. | You are starting a sick business. Your monthly costs are about 150 in rental fees. Then each pair of sock is about 3 dollars. You sell each for about 5 dollars. Write the cost function, revenue function, profit function, and estimate the amount needed to be sold in order to break even. | First you take your fixed costs being 150 and your variables which is 3 dollars. You are going to add those to get a total of 153 dollars. Then you find your revenue which is going to be 5. Then you will use the p(x)= r(x) - c(x). You plug in all your answers which is 5x-150-3x and combine like terms. This soon becomes 2x-150 and set it to zero to solve for x. You add 150 and divide by 2 to get 75. | One tip that was stuck in my head after the video is price. That is basically the organization for both profit and revenue. It is like a set up equation where you subtract. Another important fact is to remember the difference between fixed and variable costs. One meaning for utilities and the other for the actual product. | I completely understood the first concept which is being able to find the amount sold after a couple of weeks. | There is not much I'm confused on but I'm sure more practice on these concepts would come in handy. | starburstslover@gmail.com | ||||

98 | 6/28/2013 16:47:06 | Mills | Justine | First, after you read the problem, you must determine your x and y-values. You should end up with two points based upon the information given. Then, using the formula, find the slope. You can use the slope-intercept form: plug in the slope end the set of points of your choice to get b. These will all get you to the linear equation. Instead of y the equation will be f(x). When asked the quantity that was used or made, plug in the time (x-value) that is given into the linear equation you previously found. This step goes for the prediction as well. | Extrapolate means to extend something (such as a line) while assuming a linear model is being followed. An example would be to draw a line plot and draw a line between to points. The line would be extrapolated, assuming a linear model is being followed, in order to find out what is going on farther up or down the line. | Harry owns a crafts store. Here he sells things from bracelets, tie-dye, etc. Harry has started a special deal on his bracelets. During the first week of school, he had sold 15 bracelets. By the sixth week he had sold 115 bracelets. Assuming his sales follow a linear model, a) Write the linear equation to model his sales; b) calculate how many bracelets Harry sold during week 3; and c) predict how many bracelets he will sell in week 20 if this pattern continues. | First, figure out what values represent time (x-value), and what values represent amount (y-value). Once these are found, find the slope using the given numbers (x sub 1, x sub 2, y sub 1, and y sub 2). When you find the slope (m=20), plug it into y=mx+b, as well as a set of points of your choice, to find b. Once you find b, you plug that number and the slope into y=mx+b, and that is your linear equation. Instead of "y=" your equation will start with "f(x)". To calculate the amount for 3 weeks, the "f(x)" becomes "f(3)" and you plug it into the equation and solve. As for the prediction, you take the same steps. Your "f(x)" will become "f(20)" and you will plug it into the linear equation and solve for the amount of bracelets. DON'T FORGET UNITS!!! | The two different costs are variable costs. Fixed costs are paid monthly and usually stay the same. Variable costs are how much it costs to make each item. It is based on how many items you decide to produce. | Revenue is how much you charge for each item sell. Profit is when you take your revenue and subtract your costs. For example, selling an item for $10 is revenue because that is how much you charge for it. An example for profit would be taking your costs (ads, rent, how much it costs to make each item), and subtracting from the revenue. Your profit would be any extra or left-over money you have. | Harry's business is becoming well-known for his crafts store. His sale with bracelets is really getting attention. His monthly equipment for rental fees is $1200, and each bracelet is $0.25. Harry sells the bracelets for $1. Write the a) Cost function; b) Revenue Function; c) Profit Function; and d) estimate the numbers of pencils you will have to sell in order to break even (round up to the nearest pencil if necessary and find the amount of profit if you do round up). | First, you have to figure out which cost is which. The $1200 is the fixed costs and the $0.25 is the variable costs. The cost function is just the fixed costs+(variable costs)x. The cost function would then be c(x)=1200+.25x. The revenue function is just how much you sell the item for: R(x)=1x. To find the profit function, take your revenues and subtract the costs. Remember the word PRICE (P(x)=R(x)-C(x)). Plug in the corresponding values and simplify to get your profit function. To estimate the number to break even, set your profit function equal to 0 and solve. When you get the answer, if there is a decimal round up! If the there is no decimal leave it. Whether or not you rounded, plug the number into the profit function, and you will get the answer, which is usually a small profit. | Fixed costs, variable costs, revenue, profit, break-even point, linear model, and extrapolate. | The linear models and how to do them. | The business problems. Sometimes I forget to do the break-even point when you round. I forget you always round up. | justine.monique.mills@gmail.com | ||||

99 | 6/28/2013 16:36:58 | Molina | Jorge | To solve for a "linear model", one will need two sets of ordered pairs; x being the time and y being the amount. Find the slope with (y2-y1)/(x2-x1). Plug the slope and one ordered pair into the slope-intercept form y=mx+b to solve for b. Once b is solved, b-value and slope can be written in f(x)=mx+b. When solving for an amount, plug in the given time for x and solve. | "Extrapolating" means, from a given set of values, to calculate/figure-out other values with the given range. For example, if you know the total of book a bookstore sold on the first day and on the third (and assume the pattern/"slope" continues), you can extrapolate to know how much the store will sell in the future, like in a year. | Farco enjoys to eat cold desserts, especially ice-cream. In the first week, Farco had eaten 4 pints. By the eighth week, he had devoured 25 pints of ice-cream. Assuming his eating habits follow a linear model, (a) write the linear model equation for his eating of ice-cream; (b) calculate how many pints would Farco have eaten in 15 weeks; predict how many pints he would have eaten in 52 weeks (one year). | (a) To write the linear model equation, you'll first need the slope from the two given ordered pairs. (Remember: x-time, y-amount). The odered pairs are (1,4) and (8, 25); solve for the slope: (25-4)/(8-1)=21/7=3=m. Plug the slope with an ordered pair to the slope intercept form to solve for b: [4=3(1)+b] = [4=3+b]= [1=b]. Plug the slope and b-value into f(x)=mx+b; Answer: f(x)=3x+1. (b) Plug 15 into the equation to solve the pints eaten in 15 weeks. f(15)=3(15)+1. Multiply 3 and 15 (3x15=45) and add 1 (45+1=46). Answer=46 pints. (c) Plug 52 weeks into the equation to solve the number of pints Franco would have eaten in 52 weeks. f(x)=3(52)+1. Multiply 3 and 52 (3x52=156), and add 1 (156+1=157). Answer=157 pints | The two different costs we have are fixed costs and variable costs. Fixed costs are periodically, like every month. These types of costs are usually the same amount every time, like rent, advertising, etc. Variable costs, on the other hand, vary from time to time. Somtimes a product will be produced more on one month and less and the other, resulting the cost to either be more or less. | Revenue is how much charge for each item was sold. [The equation is R(x)=___(x) with the variable being the # of products/items sold]For example, a pair of average shoes can be sold for $40 each, so the revenue is $40x. Profit is the actual amount of money made with the costs/expenses paid. Take the revenues and subtract the costs: P(x)=R(x)-C(x). In a very simple example, a shoe store pays for rent and the making/ordering of shoes, but makes money from selling these shoes. Subtracting the money made and the expenses gets the profit, the actual earnings. | Farco decided to open an ice-cream store. It costs $1450 for monthly equipment and rental fees, and $2 for a gallon of ice-cream. He sells each gallon for $3.50. Write the (a) Cost Function; (b) Revenue Function; (c) Profit Function; and (d) estimate the number of gallons of ice-cream sold to break even. | (a) From reading the description, you'll know $1455 is the fixed cost (because its monthly and constant) and $2 is the variable cost (because it varies on how much he needs to buy everytime). Plug the numbers into the equation. Answer: C(x)=$1455+$2x. (b) Since Farco is selling each gallons for $3.50, it is the revenue. Answer: R(x)=$3.50x (c) Plug the cost and the revenue into the correct spots in the profit equation:[P(x)=R(x)-C(x)]. You'll get P(x)=3.5x-(1455+2x), so distibute the negative to the cost to get: P(x)=3.5x-1455-2x, and combine like terms. Answer: P(x)=1.5x-1455. (d) With the profit equation, equal it to 0 to get the BEP: 0=1.5x-1455. Add 1455 to both sides: 1455=1.5x; and then divide both sides by 1.5 to get x alone. Answer: 970 gallons. | The most important facts I need to remember are the definitions for cost, revenue, profit, and BEP. | I understood the most concept #6. | I am not confused. | alan.molina209@gmail.com | ||||

100 | 8/25/2013 19:06:21 | Molina | Moises | 1. find the two points 2. find the slope 3. plug in a point to find b 4. make the linear equation 5. answer all the questions | she used extrapolating in a form where it means expanding and she made the line longer. | Andy was collecting pennies, his mom told him every time he finds a penny its lucky so he wanted to be extra lucky. During week 1, he got 8. By week 6 he had 48 pennies. Assuming her sales follow a linear model... write the linear equation to model his collection. calculate how many pennies he had the 3rd week. and predict how many shells he will have the 13 week if the pattern continues. | First you have to find how many he is getting every week so if the first week he has 8 and 6th week he has 48 that means hes adding 8 every week. so the equation is just y=8x. then you need to plug in the 3 to the equation to find what he has in the 3rd week so its 8 times 3 and its 24. then its 8 times 13 which is 104 | Fixed cost is a cost you always have it will always stay for a certain time which is usually monthly.(EX. RENT). while variable cost which stays the same as well but it is according to the number of things you sell so if a pencil cost a dollar to make then it will stay a dollar you just dont know how many pencils you will sell a month so its a variable cost. | revenue is how much you charge for an item. for example you may see the same product like a toy but they have different prices at each store so the stores have each different revenues. Profit is any money you have leftover after you subtract cost from revenue. so the store that sells it nfor more expensive will get the most profit. | Andy has a skateboard business. it costs $1500 for monthly equipment and rental fees and it costs 25 dollars for supplies for each skateboard. Andy sells each skateboard for a 50 dollars. cost, revenue. profit, and BEP? | cost is 1500+ 25x revenue is 50x profit is 25x -1500 BEP is 60 skateboards. | cost, revenue, profit,bep, and linear models | I understood the term break even point the most. | i am still confused on how to start the problem from the first concept. | molinamoises@ymail.com |

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