Final answer:
To determine q when p is equal to 84, given that p and q vary inversely and p is 14 when q is 12, we find the constant of variation, which is 168, and then divide that by 84, resulting in q being equal to 2.
Step-by-step explanation:
If p and q vary inversely, it means that when one value increases, the other decreases in such a way that the product of the two remains constant. Given that p is 14 when q is 12, we can form the equation p * q = k, where k is the constant of variation. Thus, we have:
14 * 12 = k
Which gives us k = 168.
Now, if we want to determine q when p is equal to 84, we use the same equation with our new value of p:
84 * q = 168
Dividing both sides by 84 to solve for q, we get:
q = 168 / 84
q = 2
So, when p is equal to 84, q is 2.