If y is inversely proportional to x and y=12 when x=2, what is the value of x when y=3?

A. 2
B. 3
C. 8
D. 12

To find the value of x when y = 3, we need to use the inverse proportionality relationship between x and y.

Inverse proportionality means that as one variable increases, the other variable decreases, and their product remains constant. Mathematically, this can be expressed as xy = k, where k is a constant.

Given that y is inversely proportional to x, we can set up the proportionality equation as follows:

y = k/x

We are given that y = 12 when x = 2, so we can substitute these values into the equation:

12 = k/2

To find the value of k, we can multiply both sides of the equation by 2:

12 * 2 = k

k = 24

Now we can use this value of k to find the value of x when y = 3:

3 = 24/x

To solve for x, we can multiply both sides of the equation by x:

3x = 24

Next, divide both sides of the equation by 3:

x = 24/3

x = 8

Therefore, the value of x when y = 3 is 8.

The correct answer is C. 8.