To solve this problem, we will use the concept of inverse variation. Two quantities vary inversely if their product is constant. This means that when one quantity increases, the other quantity decreases at a rate such that the product of the two quantities remains the same.
Let's denote the constant product of p and q as k. According to the problem, when p is 2, q is 21. Therefore, we can find the constant k as follows:
k = p * q
Now plug in the values given for p and q:
k = 2 * 21
So:
k = 42
This is our constant product. Now we need to find the new value of q when p is 6. Since p and q vary inversely, we can use the constant k to find q by rearranging our original equation:
q = k / p
Substitute k with 42 and p with 6:
q = 42 / 6
Now, we perform the division:
q = 7
Therefore, when p is equal to 6, q is 7.
