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.