Given that y is inversely proportional to x and y=21 when x=6, find the value of x when y=14.

Step 1: Understand the problem The problem states that y is inversely proportional to x. This means that as x increases, y decreases and vice versa. The relationship can be expressed as y = k/x, where k is the constant of variation.

Step 2: Find the constant of variation (k) We know that y = 21 when x = 6. We can substitute these values into the equation to find k. 21 = k/6 To solve for k, we multiply both sides by 6: k = 21 * 6 k = 126

Step 3: Find the value of x when y = 14 Now that we know k, we can substitute y = 14 into the equation to find x. 14 = 126/x To solve for x, we multiply both sides by x and then divide by 14: x = 126/14 x = 9

So, when y = 14, x = 9.