# Worksheet: Inverse Variation

In this worksheet, we will practice creating formulas linking two quantities that vary directly and indirectly.

Q1:

varies inversely with . Given that when , what is the constant of proportionality?

Q2:

Decide if varies directly or inversely with and use this to find the value of when .

 𝑥 𝑦 2 4 70 70 35 2
• A420
• B
• C
• D

Q3:

For a rectangle of fixed area, the length varies inversely with its width . Given that when , determine the value of when .

Q4:

The table below shows how varies with . Use this information to find the value of when .

 𝑥 𝑦 2 7 28 28 8 2

Q5:

Given that varies inversely as , write an equation for in terms of using as a non-zero constant.

• A
• B
• C
• D

Q6:

At the beginning of the month, Jacob bought 70 eggs. Every morning he eats 2 eggs for breakfast. Is the number of remaining eggs proportional to the number of the days that have passed?

• Ayes
• Bno

Q7:

If , where is a constant, then .

• A
• B
• C
• D

Q8:

varies inversely with . Given that when , what is the constant of proportionality?

Q9:

For a rectangle of fixed area, the length varies inversely with its width . Given that when , determine the value of when .

Q10:

Sophia buys 5 liters of soda to share between the children at a party. The amount of soda each child will receive varies inversely with the number of children at the party. Write an equation for , the amount of soda in milliliters each child will receive, in terms of , the number of children at the party.

• A
• B
• C
• D
• E

Q11:

Determine the correct relation from the following choices, given that , , and .

• A
• B
• C
• D

Q12:

A group of scouts receives a donation of to fund places on an international jamboree. The amount each scout receives for their trip varies inversely with the number of scouts from the group going to the jamboree.

Write an equation for , the amount each scout receives, in terms of , the number of scouts from the group who are going to the jamboree.

• A
• B
• C
• D
• E

If 25 scouts from the group are going to the jamboree, how much will each scout receive from the donation?

Q13:

The number of hours needed for carrying out a certain task varies inversely with the number of workers who carry out the task. If the task is carried out by 23 workers in 35 hours, what is the time needed for 115 workers to carry out the task?

Q14:

A copy center is printing leaflets for a local school. The time it takes for the job to be completed varies inversely with the number of copiers used, and if 4 copiers are used, the job will take of an hour.

How many copiers are required to complete the job in half an hour?

Letting be the time in hours to complete the job using copiers, what is the value of the product, ?

Write an equation for in terms of .

• A
• B
• C
• D
• E

Q15:

If , and when , find the value of when .

Q16:

Which of the following relations represents an inverse variation between the two variables and ?

• A
• B
• C
• D

Q17:

Community groups have been invited to apply for a grant from a fund. The amount a group will receive varies inversely with the number of successful applications.

If there are 45 successful applications, each group will receive \$800.

How much will each group receive if there are 360 successful applications?

How many successful applications mean that each group receives ?

How much will each group receive if there are 150 successful applications?

What is the total value of the fund?

Write an equation for , the number of dollars each group receives when groups make successful applications.

• A
• B
• C
• D
• E

Q18:

A building contractor is constructing part of the perimeter wall for a school. The wall will be the same height all along its length. The length of time it will take to build the wall varies inversely with the number of bricklayers. A team of 12 bricklayers is expected to take 30 days to build the wall.

Write an equation for the number of days, , it would take a team of bricklayers to build the wall.

• A
• B
• C
• D
• E

How many bricklayers are required if the wall is to be finished in 20 days?

Q19:

Given that varies inversely with , and when , write an equation for in terms of .

• A
• B
• C
• D
• E

Q20:

The time taken to complete a car journey at a steady speed varies inversely with the speed of the car.

Most of the quickest route from William’s Corner to Round Rock is on the I-35. At 45 mph, this part of the journey takes 2 hours and 40 minutes.

How long would the journey take at 75 mph?

• A1 hour and 15 minutes
• B1 hour and 36 minutes
• C1 hour and 55 minutes
• D2 hours and 15 minutes
• E2 hours and 36 minutes

Write an equation for , the time it takes to cover this part of the journey at speed .

• A
• B
• C
• D
• E

How much of the route is on the I-35?

Q21:

A company making footballs decided to cut the selling price of each football by . Assuming all their footballs are identical and the same price, if they wanted to get the same amount of money from sales, by what percentage will they need to increase the number of footballs sold? Round your answer to the nearest whole number.

Q22:

varies inversely with such that . Given that when , then find the value of when .

Q23:

Suppose that is inversely proportional to and that when . Write the equation, giving in terms of .

• A
• B
• C
• D
• E

Q24:

Given that , which of the following describes the type of proportionality between and .

• A
• B
• C
• D

Q25:

Which of the following represents the relation between and ?

 𝑥 𝑦 44 55 99 110 60 75 135 150