The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages (in years) was 124. Find the present age of the son.

Explanation

Let the son's present age be x, so the father's present age is 45 − x. Five years ago, (x − 5)(40 − x) = 124. Expanding gives x² − 45x + 324 = 0, or (x − 9)(x − 36) = 0. Since the son must be younger, his present age is 9 years. The father is 36.