Question

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

Answer 1

Let the age one of the two friends be x years. 

Then the age of the other = 20 – x 

Then, 4 years ago their ages would be (x – 4) and (20 – x – 4) = 16 – x 

∴ Product of their ages 4 years ago = (x – 4) (16 – x) 

By problem (x – 4) (16 – x) = 48 

⇒ x(16 – x) – 4(16 – x) = 48 

⇒ 16x – x² – 64 + 4x = 48 

⇒ x² – 20x + 112 = 0 

Here a = 1; b = -20; c = 112

b² – 4ac = (-20)² – 4(1) (112) 

= 400 – 448 

= -48 < 0 

Thus the roots are not real. 

∴ The situation is not possible.