Question

Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Answer 1

Let the age of one friend be x years.
Age of the other friend will be (20 − x) years. 

4 years ago,
age of 1st friend = (x − 4) years
And, age of 2nd friend = (20 − x − 4) = (16 − x) years

Given that, \((x − 4) (16 − x) = 48\)
\(16x − 64 − x^2 + 4x = 48 \)
\(− x^2 + 20x − 112 = 0 \)
\(x^2 − 20x + 112 = 0 \)

Comparing this equation with \(ax^2 + bx + c = 0\), we obtain
a = 1, b = −20, c = 112

Discriminant = \(b^2 − 4ac\)
= \((− 20)^2 − 4 (1) (112)\)
= \(400 − 448\)
= \(−48 \)
As \(b^2 − 4ac < 0\), Therefore, no real root is possible for this equation and hence, this situation is not possible.