Practice Inverse Variation in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A relationship where $y = \frac{k}{x}$ : as one quantity doubles, the other halves—their product stays constant.

More workers means less time: if 4 workers take 6 hours, 8 workers take 3 hours.

Showing a random 20 of 50 problems.

Example 1

medium

A loud speaker's perceived loudness varies inversely with the square of distance. If it is

80

3

m, find loudness at

6

Example 2

medium

y=\frac{k}{x}

. If

x

is multiplied by

5

, by what factor does

y

change?

Example 3

medium

y

varies inversely with

x

, and

y = 8

when

x = 3

. Find

k

and the equation. Then find

y

when

x = 6

Example 4

easy

Can

x=0

in the inverse variation

y=\frac{k}{x}

Example 5

medium

A test pilot finds time-to-cover

1

km varies inversely with average speed. At

40

km/h it takes

90

s. Find time at

60

km/h.

Example 6

medium

y

varies inversely with

x^2

and

y=4

when

x=3

, find

y

when

x=6

Example 7

easy

y

varies inversely with

x

, and

y=3

when

x=8

. Find

y

when

x=12

Example 8

medium

y

varies inversely with

x

. Given two pairs

(2, 12)

and

(a, 4)

, find

a

Example 9

easy

Does the equation

xy = -12

describe an inverse variation?

Example 10

challenge

y=\frac{k}{x}

passes through

(2,18)

and

(a,4)

. Find

a

Example 11

hard

The pressure

P

and volume

V

of a gas at constant temperature satisfy

PV = k

. If

P = 4

atm when

V = 6

L, find

P

when

V = 8

Example 12

challenge

y

varies inversely with

x

. When

x

increases by

50\%

y

decreases by how many percent?

Example 13

easy

y = k/x

, if

x

triples, what happens to

y

Example 14

challenge

y

varies inversely with

x

. If

y

values at

x = 2

and

x = 5

differ by

9

, find

k

Example 15

challenge

Quantities satisfy

xy=k

. If

x

and

y

are positive integers and

k=24

, how many ordered pairs

(x,y)

exist?

Example 16

easy

y

varies inversely with

x

and

y = 9

when

x = 4

, find

k

Example 17

medium

It takes

6

pipes

8

hours to fill a tank. How many pipes fill it in

4

hours?

Example 18

medium

y

varies inversely with

x^2

. When

x = 2

y = 18

. Find

y

when

x = 6

Example 19

easy

y=\frac{k}{x}

, what happens to

y

when

x

doubles?

Example 20

medium

A trip takes

4

hours at

60

mph. How fast must you drive to make it in

3

hours?

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Related Concepts

Proportionality Division Rational Functions Hyperbola