Final answer:
If y varies inversely with x, we can use the equation y = k/x to solve for y when given a value for x. Using the initial values of y = 48 when x = 6, we can find the constant k. Then, we can substitute the given value of x = 18 into the equation to find y.
Step-by-step explanation:
If y varies inversely with x, this means that as x increases, y decreases, and vice versa. The inverse variation can be represented by the equation y = k/x, where k is a constant.
First, we can find the value of k using the initial values of x and y. When x = 6 and y = 48, we can substitute these values into the equation and solve for k: 48 = k/6. Multiplying both sides by 6 gives us k = 288.
Now, we can find y when x = 18 by substituting the values into the equation: y = 288/18 = 16.
Therefore, when x = 18, y = 16.