We will have 2 different equations that we will combine into 1, but we need to find the 2 k values first. If a is directly proportional to b, then a = kb. When a = 2 and b = 5, then k = 2/5. Store that for a minute. Now onto the second equation to find the other k value. If a is inversely proportional to c, then a=k/c. If a = 2 when c = 9, then k = 18. We will now use the transitive property: if a=kb and a = k/c, then kb=k/c. The k on the left is 2/5 and we are told that b = 3; the k on the right is 18 and we are looking for c. So here is what we have: [tex] \frac{2}{5} (3)= \frac{18}{c} [/tex] and [tex] \frac{6}{5} = \frac{18}{c} [/tex]. Cross multiply to get 6c = 90 and c = 15.
