The sum of the squares of the ages of Mary's two children is 289. If the boy is seven years older than the girl, what are the ages of the two children?

Question

 The sum of the squares of the ages of Mary's two children is 289. If the boy is seven years older than the girl, what are the ages of the two children?

 

Answer 1

x² + y² = 289

y = x + 7

x² + (x + 7)² = 289

2x² + 14x - 240 = 0

x² + 7x - 120 = 0

(x - 8)(x + 15) = 0

x = 8

y = 15