If m varies inversely as n and m = 8 when n = 3, find m when n = 12.

To solve this problem, we can use the formula for inverse variation, which states that m = k/n, where k is a constant.

Step 1: Find the value of k using the given information. We are told that when n = 3, m = 8. Plugging these values into the formula, we get 8 = k/3. To solve for k, we can multiply both sides of the equation by 3, giving us 24 = k.

Step 2: Now that we have the value of k, we can use it to find m when n = 12. Plugging in the values into the formula, we get m = 24/12. Simplifying this expression, we find that m = 2.

Therefore, when n = 12, m = 2.