To solve this problem, we start by understanding that if x varies inversely with y, it can be represented mathematically as:
x = k / y
where k is a constant. We need to find the value of k first, using the initial conditions provided.
Given that x = 4 when y = 8, we can substitute these values into the equation:
4 = k / 8
Now, by multiplying both sides by 8, we can solve for k:
k = 4 * 8
k = 32
Now that we have the value of k, we can find x when y = 16.
We substitute y into the original inverse variation formula:
x = 32 / 16
Calculating that gives us:
x = 2
Therefore, when y = 16, the value of x is 2.