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.

Solution:

Let’s say the age of one friend is x years.

Then, the age of the other friend will be (20 – x) years.

Four years ago,

Age of First friend = (x – 4) years

Age of Second friend = (20 – x – 4) = (16 – x) years

As per the given question, we can write,

(x – 4) (16 – x) = 48

16x – x² – 64 + 4x = 48

– x² + 20x – 112 = 0

x² – 20x + 112 = 0

Comparing the equation with ax² + bx + c = 0, we get;

a = 1, b = -20 and c = 112

Discriminant = b² – 4ac

= (-20)² – 4 × 112

= 400 – 448 = -48

b² – 4ac < 0

Therefore, there will be no real solution possible for the equations. Hence, the condition doesn’t exist.