Question

Andrew is two years older than Beatrice, and Chris is three years younger than Beatrice. The product of Andrew's age and Chris' age is 66. How old is Beatrice?

Answer 1

9

Explanation:

A = B + 2

C = B - 3

A x C = 66

A = Andrew

C = Chris

B = Beatrice

Multiply A and c together

(B + 2) x (b - 3)

b^2 - 3b + 2b - 6

b^2 -b - 6 = 66

b^2 - b - 72 = 0

factors of -72b^2 that add up to - b are -9b + 8b

b^2 + 8b -9b - 72

b (b + 8) -9(b + 8)

b = 9 or - 8

b = 9