WAEC Mathematics 2025 Theory question 102

Theory question 102

Quadratic Equations

The product of the ages of Adu and Tanko is 9 less than Akorfa's age. If Tanko is 4 years older than Adu and Akorfa's age is six times Tanko's age, find Akorfa's age.

Show the model answer

Model answer

Let Adu = x, Tanko = x + 4, Akorfa = 6(x + 4)
x(x + 4) + 9 = 6(x + 4) ⇒ x² − 2x − 15 = 0 ⇒ (x − 5)(x + 3) = 0 ⇒ x = 5
Tanko = 9, so Akorfa = 54 years

Explanation

Ages are positive, so reject x = −3.