NECO 2024 · Paper 1 · Q33

Quadratics & their graphs

The difference between the present ages of two brothers is 6 and their product is 135. What is the sum of their ages?

Worked solution (try it first)

Let the younger brother be $x$ , so the older is $x + 6$ .
Their product is $x(x + 6) = 135$ .
Rearrange: $x^2 + 6x - 135 = 0$ , which factorises as $(x - 9)(x + 15) = 0$ .
An age is positive, so $x = 9$ and the ages are 9 and 15.
So the sum of their ages is $9 + 15 = 24$ , option B.

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