TODAY’S LESSON
Solving Word Problems Involving Direct Proportion
OBJECTIVE
The learner solves problems involving direct proportion
READING DRILL:
COUNTING THE RAIN
I love counting the rain, Mother. Ashley patter and as I see. Do not all the great men like Rizal count rain, too, when still young like me?
See the numerous dropping rains
How hard it is for little brains.
And I recall the children’s riddle
About the old man’s countless canes
How I love the fast-falling rain
Like a thousand pounding pestles
And the little rushing water
Down the stream to see it nestles.
KING BACK
L
How do you solve for the missing means or extreme in a proportion?
What do you usually do during weekends?
PROBLEM OPENER
Roy and Al sell newspapers on weekends to earn extra money. For every 3 newspapers that Roy sells, Al sells 5. If Roy sold 15 newspapers, how many did Al
sell?
Analyze the problem.
a.) What is asked in the problem?
b.) What are given?
c.) Illustrate the problem.
Roy
Al
Note that the quantities change in the same direction. As the number of newspapers that Roy sells increases, the number of newspapers that Al sells also increases. This proportion is called DIRECT PROPORTION.
In direct proportion, when one quantity increases, the other quantity increases at the same rate and vice versa.
To solve word problems with direct proportion:
-List down the given facts and identify the missing term.
-Set the proportion for the problem.
-Solve for the missing term.
EXERCISE 1
Work in groups. Illustrate the problem and write the proportion.
The sign on the store window says, “Magazine for sale, buy 3, take 2.” How many magazines must I buy If I want to take 10 magazines for free?
EXERCISE 2
Solve the problems.
a) A motorist travels 275 km in 5 hours. How far can he travel in 9 hours at the same speed?
Proportion: __________
Answer: __________
b)Two buses can transport 130 people. How many buses are needed to transport 780 pupils?
Proportion: __________
Answer: __________
EXERCISE 3
Read and solve.
What have you learned?
A S S E S S M E N T
Analyze each problem and write a proportion to solve it. Draw a diagram to help you when necessary.
1) A tree casts a shadow of 12 meters when a 5-metre pole casts a shadow of 4 meters. How tall is the tree?
2) At the rate of 3 items per 100, how much will 12 items cost?
3) A car travels 72 km on 8 liters of gasoline. At the same rate, about how far can it travel on 11 liters of gasoline?
A S S I G N M E N T
Write a proportion for each problem, then find the missing term.
a) The ratio of 2 numbers is 3:5. The larger number is 30. What is the smaller number?
b) There are 3 teachers to 125 pupils during the school program. How many teachers were
there if there were 2 500 pupils?
c) The ratio of male teachers to female teachers in our school is 2:9. If there are 108 female teachers, how many teachers are male?
TODAY’S LESSON
Solving Word Problems Involving Partitive Proportion
OBJECTIVE
The learner solves problems involving partitive proportion
READING DRILL:
COUNTING THE RAIN
I love counting the rain, Mother. Ashley patter and as I see. Do not all the great men like Rizal count rain, too, when still young like me?
See the numerous dropping rains
How hard it is for little brains.
And I recall the children’s riddle
About the old man’s countless canes
How I love the fast-falling rain
Like a thousand pounding pestles
And the little rushing water
Down the stream to see it nestles.
KING BACK
L
How do we solve word-problems involving direct proportion?
Do you share your baon to your friends? How?
PROBLEM OPENER
Joy and Dale are twins. They always share their things equally. Even their mother gave them the same amount of anything, whether money, toys, candies, and others. But one day, their father gave them 5 chocolates, 2 chocolates for Joy and 3 chocolates for Dale.
Analyze the problem.
a.) What do you think each of the girls felt?
b.) Why did their mother give them things equally?
c.) If you were one of the girls, what will you do?
d.) Is it right to have the same amount of things as your other siblings? Why?
Joy and Dale found out that there are things that cannot be shared equally. So one day, their mother gave them P150 so that the ratio is 2:3, 2 parts for Dale and 3 parts for Joy. How much did each girl receive?
PARTITIVE PROPORTION
In partitive proportion, a whole is divided into parts that is proportional to the given ratio.
To solve word problems involving partitive proportion, divide the given total or difference by the sum or difference of the ratio, then multiply the answer by each of the terms.
EXERCISE 1
Analyze and solve each problem.
2. The ratio of chairs to tables is 2:7. There are 180 chairs and tables in a party. How many are there of each kind?
3. The sum of two numbers is 215. If the ratio is 2:3, find the larger number.
EXERCISE 2
Analyze and solve each problem.
1. Two numbers are in the ratio of 4:7. If the sum is 330, what are the numbers?
2. The ratio of Math books to Filipino books in a class is 8 to 5. How many Math books are there if there are 247 books in all?
3. The difference of two numbers is 12. Find the numbers if their ratio is 1:2.
EXERCISE 3
Solve the given problems.
1) The salary of two workers is in the ratio 3:4. They received 12,250.00. How much did each worker receive?
2) The ratio of men to women at a college is 7 to 5. How many women students are there if there are 350 men?
3) The ratio of Math books to other books in a class is 8 to 5. How many Math books are there if there are 247 books in all?
What have you learned?
A S S E S S M E N T
Read and analyze, then solve the problems.
1) The ratio of cats to dogs is 6:5. There are 495 dogs and cats in a certain barangay.
b) How many dogs are there?
2) Three numbers are in the ratio 2:5:7. If their sum is 504, what are the three numbers?
a) first number
b) second number
c) third number
A S S I G N M E N T
Analyze and solve the problems carefully.
1) The ratio of doors to windows is 1:5. There are 186 doors and windows in a building. How many
doors are there? windows?
2) The ratio of the angles of a triangle is 3:4:5. Find the measure of each angle.
3) Three numbers are in the ratio 1:4:7. Find the second number if their sum is 276.
4) The difference between two numbers is 40. They are in the ratio 9:7. What are the numbers?
TODAY’S LESSON
Solving Word Problems Involving Inverse Proportion
OBJECTIVE
The learner solves problems involving inverse proportion
READING DRILL:
COUNTING THE RAIN
I love counting the rain, Mother. Ashley patter and as I see. Do not all the great men like Rizal count rain, too, when still young like me?
See the numerous dropping rains
How hard it is for little brains.
And I recall the children’s riddle
About the old man’s countless canes
How I love the fast-falling rain
Like a thousand pounding pestles
And the little rushing water
Down the stream to see it nestles.
KING BACK
L
How do we solve word-problems involving partitive proportion?
Have you visited some of the places that care for the physically handicapped, aged, orphans, etc. Why are these places important?
PROBLEM OPENER
I have enough money for a vacation of 12 days if I spend 500 a day. For how many days will my money last if I decide to spend only 400 a day.
Analyze the problem.
a) What is asked?
b) What are given?
c) How can we solve the problem?
An orphanage has enough bread to feed 30 orphans for 12 days. If 10 more orphans are added, how many days will the same amount of bread last?
Analyze the problem:
a) What is asked?
b) What are given?
c) How can we solve the problem?
INVERSE/INDIRECT PROPORTION
Two quantities are in inverse proportion when one quantity decreases (or increases) in a certain ratio, the other quantity will then increase (or decrease) in the inverse of that ratio.
EXERCISE 1
Analyze and solve each problem.
2) Twelve painters can paint a building in 10 days. How many painters are needed to paint
it in 6 days?
EXERCISE 2
Analyze and solve each problem.
If 8 men can build a house in 90 days, in how many days can 20 men working under the same conditions as the 8 men build the house?
EXERCISE 3
Solve the given problems.
A carpenter working 8 hours a day could finish a piece of work in 6 days. How many days could he finish a similar piece of work by working 10 hours a day?
What have you learned?
A S S E S S M E N T
Set the following proportions and solve.
1) A stock of food is enough to feed 50 persons for 14 days. How many days will the food last if 20 more persons will be added?
2) Four equal pumps can fill a tank in 42 minutes. How long will 6 pumps of the same kind fill the tank?
3) If 3 farmers can plow a field in 4 days, how long will 6 farmers do it?
4) Five sewers can finish 200 children’s dresses in 8 days. How many days will it take 10 sewers to finish the same number of children’s dresses?
5) Three pipes take 60 minutes to water the field. How much time it will take to water the field with 6 pipes?
A S S I G N M E N T
Solve these problems.
2) Sixty boxes are needed to pack 720 brownies in batches of 12. How many boxes are needed if the brownies are packed in batches of 18?
3) Mr. Datu has enough money to pay 8 workers for 15 days. If he adds 4 more workers, for how long can he pay them at the same rate?
TODAY’S LESSON
Solving Word Problems Involving Direct Proportion, Partitive Proportion, and Inverse Proportion
OBJECTIVE
The learner solves problems involving direct, partitive, and inverse proportions
READING DRILL:
COUNTING THE RAIN
I love counting the rain, Mother. Ashley patter and as I see. Do not all the great men like Rizal count rain, too, when still young like me?
See the numerous dropping rains
How hard it is for little brains.
And I recall the children’s riddle
About the old man’s countless canes
How I love the fast-falling rain
Like a thousand pounding pestles
And the little rushing water
Down the stream to see it nestles.
KING BACK
L
What are the three types of proportions?
Who among you know someone who is working as salesman or saleswoman? Can you describe the qualities of being a salesman or saleswoman?
PROBLEM OPENER
1. It takes 3 salesmen 8 days to sell 5,000 boxes of soap. If 2 more salesmen are added, how long will it take them?
Analyze the problem.
a) What is asked?
b) What are given?
c) How can we solve the problem?
PROBLEM OPENER
2. If 3 eggs cost P8.00, how much will 12 eggs cost?
PROBLEM OPENER
3. Three boys sold garlands in the ratio 2:3:4. Together they sold 225 garlands. How many garlands did each boy sell?
PROBLEM OPENER
4. A basket of food is sufficient to feed 15 persons for 3 days. How many days would it last for 10 persons?
PROBLEM OPENER
5. The ratio of Math books to Filipino books in a class is 8 is to 5. How many Math books are in if there are 247 books in all?
EXERCISE 1
Answer the following problems and tell whether the proportion is direct, partitive, or inverse.
1. Chris earns P5000.00 in 20 days. How much will he earn in 30 days?
5000:20 = N:30
EXERCISE 1
Answer the following problems and tell whether the proportion is direct, partitive, or inverse.
2. Ann, Jane and May shared 360 stamps in the ratio of 3:4:5. How many stamps did Ann get?
EXERCISE 1
Answer the following problems and tell whether the proportion is direct, partitive, or inverse.
3. If 50 persons can consume a certain amount of food in 2 months, in how many months can 30 persons consume the same amount of food?
EXERCISE 2
Analyze and solve each problem.
1. If 6 men can paint a wall in 64 hours, find the number of men required to paint the wall in 48 hours.
EXERCISE 2
Analyze and solve each problem.
2. A farmer has enough feeds for 72 ducks for 14 days. If he sells 16 ducks, how long will the feeds last?
EXERCISE 2
Analyze and solve each problem.
3. Alex can finish reading a novel in 3 days. How many novels can he finish in 1 month if there are 30 days in that month?
EXERCISE 3
Read, analyze, and solve each problem.
1.) At the price of 3 guavas for P12.60, how many guavas can be bought for P37.80?
EXERCISE 3
Read, analyze, and solve each problem.
2.) How much prize will each winner get if a cash prize of P45000 will have to be divided in the ratio of 1:3:5?
3.) Four machines can recopy 25000 books in 6 days. How many machines are needed to copy 25000 books in 3 days?
EXERCISE 3
Read, analyze, and solve each problem.
4.) If 4 people can paint a fence in 3 hours. How long will it take 6 people to paint it?
5.) If 12 workers can build a wall in 10 hours, how long do 5 workers build a wall?
What are the differences among the three types of proportions?
What have you learned?
A S S E S S M E N T
Solve the following:
1.) Mr. Franco mixes 3 bags of sand with every 2 bags of cement. How many bags of sand should be mixed with 8 bags of cement?
2.) A motorist traveled 240km in 3 hours. At that rate, how long will it take to travel 400km?
3.) Find two numbers in the ratio of 2:5 and their difference is 18.
4.) Three writers can do the worktext in twelve months. How long can six writers do the same job?
5.) Four equal pumps working together can fill a swimming pool in 9 hours. How long would 3 equal pumps working together fill the same swimming pool?
A S S I G N M E N T
Solve these problems.
1.) The ratio of girls to boys in Ronald’s school is 3:4. The school has 228 boys. How many are girls?
2.) The difference of two numbers is 12. Find the numbers if their ratio is 1:2.
3.) If a certain amount of work is done by 9 men, 6 women and 3 boys in 10 days, how long will the same work rate if 18 men, 12 women, and 6 boys are set to do the task?
WEEKLY ASSESSMENT