Question

Suppose y varies inversely with x, and y = 18 when x = 12. What is the value of x when y = 24? NO LINKS OR ANSWERING YOU DON'T KNOW?

a. 24
b. 9
c. 12
d. 18​

Answer 1

B. 9

Explanation:

We are given that y varies inversely with x. Recall that inverse variation has the form:

`\displaystyle y=(k)/(x)`

Where k is the constant of variation.

We are given that y = 18 when x = 12. Hence:

`\displaystyle (18)=(k)/((12))`

Solve for k. Multiply both sides by 12:

`k=12(18)=216`

Thus, our equation is:

`\displaystyle y=(216)/(x)`

We want to find x when y = 24. Substitute:

`\displaystyle (24)/(1)=(216)/(x)`

Cross-multiply:

`24x=216`

Divide both sides by 24. Hence:

`x=9`

Our answer is B.

Answer 2

B

Explanation:

Given that y varies inversely with x then the equation relating them is

y =
`(k)/(x)` ← k is the constant of variation

To find k use the condition y = 18 when x = 12 , then

18 =
`(k)/(12)` ( multiply both sides by 12 )

216 = k

y =
`(216)/(x)` ← equation of variation

When y = 24 , then

24 =
`(216)/(x)` ( multiply both sides by x )

24x = 216 ( divide both sides by 24 )

x = 9