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Worksheet: Inverse Variation and its Applications

Q1:

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

Q2:

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

Q3:

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

Q4:

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

  • A
  • B
  • C
  • D

Q5:

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

Q6:

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?

Q7:

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

  • A
  • B
  • C
  • D

Q8:

The current in a circuit varies inversely with the circuit’s resistance, measured in ohms. When the current is 40 amperes, the resistance is 10 ohms. Find the current if the resistance is 12 ohms. Round your answer to two decimal places if necessary.

Q9:

The rate of vibration of a string under constant tension varies inversely with the length of the string. If a string is 24 inches long and vibrates 128 times per second, what is the length of a string that vibrates 64 times per second?

Q10:

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?

Q11:

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

  • A
  • B
  • C
  • D
  • E

Q12:

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

  • A
  • B
  • C
  • D
  • E

Q13:

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

Q14:

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

Q15:

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

2 4 70
70 35 2
  • A
  • B420
  • C
  • D

Q16:

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

2 7 28
28 8 2