Direct & Inverse Variation

Problem: 1

Given that the variables vary directly, write an equation relating x and y.

x = 6, y = 18

Problem: 3

Given that the variables vary directly, write an equation relating x and y.

x = 5, y = 20

Problem: 5

Given that the variables vary directly, write an equation relating x and y.

x = 21, y = 3.

Problem: 7

Given that the variables vary directly, write an equation relating x and y.

x = 6.9, y = 2.3.

Problem: 9

Given that the variables vary directly, write an equation relating x and y.

x = –4, y = –2.

Problem: 11

Given that the variables vary directly, write an equation relating x and y.

x = –16, y = 4.

Problem: 13

A paycheck varies directly with the number of hours worked.

Suppose the pay for 20 hours of work is $238.25.

What is the pay for 500 hours of work?

Problem: 15

Your weight on Mars varies directly with your weight on Earth. A person weighing 125 lb on Earth weighs 47.25 lb on Mars, since Mars has less gravity.

If you weigh 155 lb on Earth, how much will you weigh on Mars?

Problem: 17

On the world map, the distance between the cities of Baconburg and Hamfat is 12 inches.

Each inch on the map represents 400 miles.

How far away are Baconburg and Hamfat actually?

Problem: 19

Write an equation of variation for y = 30 when x = 5, where y varies inversely as x.

Problem: 21

Write an equation of variation for y = 0.225 when x = 20, where y varies inversely as x.

Problem: 23

Write an equation of variation for y = 54 when x = 36, where y varies inversely as x.

Problem: 25

Write an equation of variation for y = 0.4 when x = 0.7, where y varies inversely as x.

Problem: 27

Write an equation of variation for y = 0.6 when x = 8, where y varies inversely as x.

Problem: 29

Write an equation of variation for y = ⁴/₇ when x = ⁷/₄, where y varies inversely as x.

Problem: 31

It takes 4 people 10 hours to resurface a stretch of road. How long will it take

8 people to do the same job?

Problem: 33

The volume V of a gas varies inversely as the pressure p on it.

If the volume is 300 cm³ under a pressure of 48 kg/cm², what is the volume under a pressure of 25 kg/cm²?

Problem: 35

A pump empties a swimming pool in 60 minutes at the rate of 1500 L/min.

If the rate of pumping is 2500 L/min, how long does it take to empty the swimming pool?

Problem: 37

The number of miles you drive in your tractor, d, in t hours is given by d = 13t.

Is this an instance of direct variation, inverse variation, or neither?

Problem: 39

The number u of candy bars Roxanne ate at lunch and the number v of candy bars she can eat after dinner are related by u = k + v.

Is this an instance of direct variation, inverse variation, or neither?

Problem: 1

Given that the variables vary directly, write an equation relating x and y.

x = 6, y = 18

Problem: 3

Given that the variables vary directly, write an equation relating x and y.

x = 5, y = 20

Problem: 5

Given that the variables vary directly, write an equation relating x and y.

x = 21, y = 3.

Problem: 7

Given that the variables vary directly, write an equation relating x and y.

x = 6.9, y = 2.3.

Problem: 9

Given that the variables vary directly, write an equation relating x and y.

x = –4, y = –2.

Problem: 11

Given that the variables vary directly, write an equation relating x and y.

x = –16, y = 4.

Problem: 13

A paycheck varies directly with the number of hours worked.

Suppose the pay for 20 hours of work is $238.25.

What is the pay for 500 hours of work?

Problem: 15

Your weight on Mars varies directly with your weight on Earth. A person weighing 125 lb on Earth weighs 47.25 lb on Mars, since Mars has less gravity.

If you weigh 155 lb on Earth, how much will you weigh on Mars?

Problem: 17

On the world map, the distance between the cities of Baconburg and Hamfat is 12 inches.

Each inch on the map represents 400 miles.

How far away are Baconburg and Hamfat actually?

Problem: 19

Write an equation of variation for y = 30 when x = 5, where y varies inversely as x.

Problem: 21

Write an equation of variation for y = 0.225 when x = 20, where y varies inversely as x.

Problem: 23

Write an equation of variation for y = 54 when x = 36, where y varies inversely as x.

Problem: 25

Write an equation of variation for y = 0.4 when x = 0.7, where y varies inversely as x.

Problem: 27

Write an equation of variation for y = 0.6 when x = 8, where y varies inversely as x.

Problem: 29

Write an equation of variation for y = ⁴/₇ when x = ⁷/₄, where y varies inversely as x.

Problem: 31

It takes 4 people 10 hours to resurface a stretch of road. How long will it take

8 people to do the same job?

Problem: 33

The volume V of a gas varies inversely as the pressure p on it.

If the volume is 300 cm³ under a pressure of 48 kg/cm², what is the volume under a pressure of 25 kg/cm²?

Problem: 35

A pump empties a swimming pool in 60 minutes at the rate of 1500 L/min.

If the rate of pumping is 2500 L/min, how long does it take to empty the swimming pool?

Problem: 37

The number of miles you drive in your tractor, d, in t hours is given by d = 13t.

Is this an instance of direct variation, inverse variation, or neither?

Problem: 39

The number u of candy bars Roxanne ate at lunch and the number v of candy bars she can eat after dinner are related by u = k + v.

Is this an instance of direct variation, inverse variation, or neither?

Hotmath Practice Problems

Section 3-3

Direct and Inverse Variation