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If p and q vary inversely and p is 14 when q is 12, determine q when pins equal to 84.

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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.

User Sergey Grishchev
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