Tips and Markups
Copyright © McGraw Hill
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Solve each problem.
1. A bagel shop sold 81 of their 108 bagels on Monday. What percent of the bagels did they sell?
2. Keana has visited 19 of the 50 states in the U.S. What percent of the states has she visited?
3. Of the 20 students in a class, 14 wore tennis shoes to school today. What percent of the students wore tennis shoes?
Warm Up
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Solve each problem.
1. A bagel shop sold 81 of their 108 bagels on Monday. What percent of the bagels did they sell? 75%
2. Keana has visited 19 of the 50 states in the U.S. What percent of the states has she visited? 38%
3. Of the 20 students in a class, 14 wore tennis shoes to school today. What percent of the students wore tennis shoes? 70%
Warm Up
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
7.RP.A.3
Use proportional relationships to solve multistep ratio and percent problems.
7.EE.A.2
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.
Standards for Mathematical Content
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
7.EE.B.3
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
Standards for Mathematical Content
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
MP1
Make sense of problems and persevere in solving them.
MP2
Reason abstractly and quantitatively.
MP3
Construct viable arguments and critique the reasoning of others.
Standards for Mathematical Practice
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
MP4
Model with mathematics.
MP7
Look for and make use of structure.
Standards for Mathematical Practice
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Students will solve multi-step ratio and percent problems involving tips and markups.
Lesson Goal
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
A tip, or gratuity, is an additional amount of money paid in return for a service. This amount is sometimes a percent of the service cost. The total amount paid is the cost of the service plus the tip.
Learn
Tips
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Example 1�Tips
The bill for a group of eight people at a restaurant was $125 before the tip was added. The group wants to add an 18% tip.
What will be the total bill including the tip?
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Example 1�Tips
Think About It!
What is a good estimate for the solution? Explain how you calculated the solution.
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Example 1�Tips
Write a proportion. Then solve using ratio reasoning. Let t represent the amount of the tip.
Method 1 Use ratio reasoning.
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Example 1�Tips
Add the tip to the bill. The total cost is $125 + $22.50, or $147.50.
amount of tip
amount of bill
Percent
Because 100 × 1.25 = 125, multiply 18 by 1.25 to find the value of t.
18 × 1.25 = 22.50, so, t = 22.50.
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Example 1�Tips
Method 2 Use properties of operations. Let t represent the amount of the tip.
Add the tip to the bill. The total cost is $125 + $22.50, or $147.50. So, using either method, the total cost of the bill is $147.50.
| Write the proportion. |
| Divide 18 by 100. A one-step equation results. |
| Multiplication Property of Equality |
t = 22.50 | Simplify. |
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Example 1�Tips
Talk About It!
How could you solve the problem another way?
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Check
Amy wants to tip her hairstylist 20% for a haircut that costs $48. What is her total bill with tip? Use any strategy.
Example 1�Tips
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Check
Amy wants to tip her hairstylist 20% for a haircut that costs $48. What is her total bill with tip? Use any strategy.
$57.60
Example 1�Tips
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
In order to make a profit, stores typically sell items for more than what they pay for them. The amount the store pays for an item is called the wholesale cost. The amount of increase is called the markup. The selling price is the amount the customer pays for an item. The selling price is equal to the wholesale cost plus the markup.
selling price = wholesale cost + markup
Learn
Markup
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Example 2�Markup
The wholesale cost for each shirt at a clothing store is $17. The store manager plans to mark up the shirts by 125%.
What will be the selling price for each shirt?
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Example 2�Markup
Think About It!
What is a good estimate for the solution? Explain how you calculated that estimate.
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Example 2�Markup
Write a proportion. Then solve using ratio reasoning. Let x represent the selling price.
Method 1 Use ratio reasoning.
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Example 2�Markup
Add the markup to the wholesale cost. The selling price is $17 + $21.25, or $38.25.
amount of markup
wholesale cost
Percent
Because 100 × 0.17 = 17, multiply 125 by 0.17 by to find the value of x.
125 × 0.17 = 21.25, so, t = 21.25.
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Example 2�Markup
Method 2 Use properties of operations.
Add the markup to the wholesale cost. The selling price is $17 + $21.25, or $38.25. So, using either method, the selling price is $38.25.
| Write the proportion. Let x represent the markup. |
| Divide 125 by 100. A one-step equation results. |
| Multiplication Property of Equality |
x = 21.25 | Simplify. |
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Example 2�Markup
Talk About It!
Compare the wholesale cost with the selling price. How do you know the selling price is reasonable?
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Example 2�Markup
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Example 2�Markup
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Example 3�Markup
Ben’s family is shopping for a new car. The selling price of a car is $24,199.50. Ben researches to find that the wholesale cost of the car is $22,100.00.
What is the percent of markup?
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Example 3�Markup
Think About It!
What is a good estimate for the solution? Explain how you calculated that estimate.
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Example 3�Markup
Step 1 Identify the part and the whole.
original amount = $22,100.00 | This is the whole. |
new amount = $24,199.50 | This is the whole plus the part. |
amount of increase = $2,099.50 | This is the part. |
Finding the percent of markup is the same as finding the percent of increase.
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Example 3�Markup
Step 2 Find the percent of increase.
| Write the part-to-whole ratio. The part is 2,099.50. The whole is 22,100.00. |
= 0.095 | Divide. |
| Write an equivalent ratio, as a rate per 100. |
= 9.5% | Definition of percent |
So, the percent of markup for the wholesale price of the car is 9.5%.
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Example 3�Markup
Talk About It!
How is finding the percent of markup different than finding the selling price of an item?
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Check
Mikka is making jewelry for a craft show. The wholesale cost of a bracelet is $12.50. If she sells them for $20, what is the percent of markup?
Example 3�Markup
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Check
Mikka is making jewelry for a craft show. The wholesale cost of a bracelet is $12.50. If she sells them for $20, what is the percent of markup?
60%
Example 3�Markup
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Pause and Reflect
Compare and contrast tips and markups. Where have you seen or used tips and markups in your everyday life?
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Apply�Dining Out
Pizza | $18.60 |
Salad | $2.50 |
Soda | $2.25 |
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Apply�Dining Out
Talk About It!
What steps should you take before splitting the bill?
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Check
Brian has $24 worth of pizza delivered to his house. He pays the bill plus a 15% tip and 7% sales tax. He also pays a $3 delivery fee that is charged after the tax and tip. How much change does he receive, if he pays with two $20 bills?
Apply�Dining Out
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Check
Brian has $24 worth of pizza delivered to his house. He pays the bill plus a 15% tip and 7% sales tax. He also pays a $3 delivery fee that is charged after the tax and tip. How much change does he receive, if he pays with two $20 bills?
$7.72
Apply�Dining Out
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Pause and Reflect
Explain how tips and markups are percents of increase.
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Exit Ticket
Suppose you had lunch with a friend at a restaurant. The lunch cost $32.00, and sales tax was $4.45. If you plan to tip 20%, find the total amount you need to pay for lunch. Write a mathematical argument that can be used to defend your solution.
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.
Exit Ticket
Suppose you had lunch with a friend at a restaurant. The lunch cost $32.00, and sales tax was $4.45. If you plan to tip 20%, find the total amount you need to pay for lunch. Write a mathematical argument that can be used to defend your solution.
$42.85; Sample answer: Find 20% of $32.00, which is $6.40. Add $6.40 to $32.00, which is $38.40. Then add the sales tax of $4.45. $38.40 + $4.45 = $42.85
McGraw Hill |
Tips and Markups
This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.