a woman is 3 times as old as her son. 8 years ago the product of their ages was 112. find their present ages

Son 12 and woman 36 years old.

Step-by-step explanation:

Let the age of the woman now be 3x years, then her son's age = x years.

8 years ago the woman's age was (3x-8) and her son's age was (x - 8) years, so:

(3x - 8) (x - 8) = 112

3x^2 - 32x + 64 = 112

3x^2 - 32x - 48 = 0

3x^2 - 36x + 4x - 48 = 0

3x (x - 12) + 4 (x - 12) = 0

(3x + 4) (x - 12) = 0

x = - 1.33 ..., 12. (We ignore the negative value).

So the son's age is 12 and the woman's age is 36.