The sum of the present ages of a father and his son is years
MATHEMATICS · Multi-part · AoPS · Mathematics · Quadratic Equations - Part 2 · Quadratic Equations - Part 2
Problem
The sum of the present ages of a father and his son is 45 years. Five years ago, the product of their ages was 250 years.
Work out the following:
(i) Taking the present age of the father to be x years, express the present age of the son in terms of x and write the relation obtained from the condition given for their ages five years ago.
(ii) Reduce the relation obtained in part (i) to a quadratic equation in x and solve it to find the present ages of both father and son.
(iii) State clearly which root corresponds to the father's age and which to the son's age, giving a brief reason for your choice.