Question

Ben Better is 5 years older than his sister Ima. All they will tell you is that the sum of the squares of their age is 773. How old are they?

Answer 1

17 and 22yrs

Explanation:

Given parameters:

Let Ben's age = B

Let Ima's age = L

B = L + 5 -----i

Also,

the square of their age is 773;

B² + L² = 773 ---ii

To find their ages, substitute equation i into ii;

(L + 5)² + L² = 773

L² + 10L + 25 + L² = 773

2L² + 10L + 25 = 773

2L² + 10L + 25 - 773 = 0

2L² + 10L -748 = 0

Divide through by 2;

L² + 5L - 374 = 0

L² + 22L - 17L - 374 = 0

L(L + 22) - 17(L + 22) = 0

(L - 17)(L + 22) = 0

L = 17 or -22

Age cannot be -22;

Ima's age = 17

Ben's age;

B = L + 5

B = 17 + 5 = 22