6.3 Inverse Proportion
Answer the following questions:

A. Find the value of N so that the given ratios are directly proportional.
1. 5: 12 and N: 24
2. N: 5 and 14: 35
3. 11/6 and N/30
4. 7/N and 42/66

B. 1. If the ratio 8 ∶ 15 is inversely proportional to 10 ∶ N, what is the value of N?

2. The ratio 11/20 is inversely proportional to m/5. Find the value of m.

3. The ratio 5 ∶ M is directly proportional to 15 ∶ 6 but is inversely proportional to
10 ∶ N. Find the values of M and N.

4. A soap factory can produce 5000 units of soap in two days if five machines are used. How many units can be made in five days if 10 machines are used?

C. Find the value N so that the given ratios are inversely proportional.
1. 14 ∶ 5 and 10 ∶ N
2. N ∶ 33 and 9 ∶ 11
3. 15/19 and N/27
4. 6/N and 2/39

D. 1. Six pipes are needed to fill a tank in 1 hour and 20 minutes. How long will it take if only 4 pipes of the same type are used?

2. There are 50 students in a hostel. Food provided for them is good only for 40 days.
How long will the same amount of food last if 30 more students join the group?

3. Five trucks can transport 120 tons of goods in 2 days. How many tons of goods
can 3 trucks transport in 4 days?

4. In a central post office, 4 machines categorize 8 000 packages in 8 hours. How
many machines are needed to categorize 4 500 packages in 6 hours?

6.4 Partitive Proportion
Answer the following questions:

A. Consider having numbers from 1–20. Write the ratio representing the following (express in the simplest term, if possible):

1. Odd numbers to all numbers involved
2. Numbers divisible by 5 to even numbers
3. Numbers greater than 7 to numbers less than 12
4. Even numbers greater than 5 but less than 17 to all numbers involved

B. 1. Two numbers are in the ratio of 8: 9. Their sum is 136. What are the numbers?

2. Three numbers are in the ratio of 3: 2: 7. Their sum is 108. What are the numbers?

3. Four numbers are in the ratio 5: 6: 7: 8. The greatest of these is 24. Find the sum of
these numbers.

4. A piece of land was divided among three heirs. The eldest heir received three times as much as the youngest child, who received two times as much as the middle child. If the middle child received 12 hectares (ha) of land, what was the total area of land did they inherit?

C. 1. The ratio of a set of numbers is given as well as their sum. Find the numbers.
1. The numbers are in the ratio 4: 5 and their sum is 108.
2. The numbers are in the ratio 6: 7: 8 and their sum is 63.

2. The ratio of a set of numbers is given. One of the numbers is also given. Find the sum of the numbers.
1. The numbers are in the ratio 2: 3: 5. The least of these is 48.
2. The numbers are in the ratio 3: 5: 7. The greatest of these is 75.

D. Solve the following problems. Show your complete solution.

1. A class has 50 students. The ratio of males to females is 2: 3. How many males and
female students are there?

2. Cherie, Mona, and Kate shared 360 stamps in the ratio of 3: 4: 5, respectively. How
many stamps did each of them have?

3. Forty marbles are in a bag. The ratio of red to yellow to blue to green marbles is
1: 2: 2: 3, respectively. How many of the marbles are colored yellow or green?

4. A tall shelf has 80 books. The ratio of fiction to nonfiction to a general reference to
children’s books is 6: 5: 2: 3, respectively. How many more children’s books are
there than general reference books?