Sally's cat is 3 years older than Helen's dog. The product of their ages is 54. How old is Helen's dog?

A.

9

B.

6

C.

25

D.

29

The first thing that we have to do is to assign variables to the cat's and the dog's ages. Let us use c to represent the age of the cat and d for the dog's age. So, let's translate the word problem into a mathematical one.

c = d + 3

This is the first equation while the second equation is

(d+3) * d = 54

which becomes

d^2 + 3d - 54 = 0

which can be factored into (d-6) (d+9). This gives us two roots which are 6 and - 9. However, age is a non-negative number so we will take 6 as the age of Helen's dog. Thus, making Sally's cat 9 years old.