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

Answer:

B

Step-by-step explanation:

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

y = $\frac{k}{x}$ ← k is the constant of variation

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

18 = $\frac{k}{12}$ ( multiply both sides by 12 )

216 = k

y = $\frac{216}{x}$ ← equation of variation

When y = 24 , then

24 = $\frac{216}{x}$ ( multiply both sides by x )

24x = 216 ( divide both sides by 24 )

x = 9

Answer 2

Answer:

B. 9

Step-by-step explanation:

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

$\displaystyle y=\frac{k}{x}$

Where k is the constant of variation.

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

$\displaystyle (18)=\frac{k}{(12)}$

Solve for k. Multiply both sides by 12:

$k=12(18)=216$

Thus, our equation is:

$\displaystyle y=\frac{216}{x}$

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

$\displaystyle \frac{24}{1}=\frac{216}{x}$

Cross-multiply:

$24x=216$

Divide both sides by 24. Hence:

$x=9$

Our answer is B.