Question 190217
    The sum of the squares of Maria's two kids is 289. If the boy is seven years older than the girl, then what are their ages ?
.
Let g = age of the girl
then
g+7 = age of boy
.
g^2 + (g+7)^2 = 289
g^2 + (g+7)(g+7) = 289
g^2 + (g^2+14g+49) = 289
2g^2 + 14g + 49 = 289
2g^2 + 14g - 240 = 0
g^2 + 7g - 120 = 0
(g+15)(g-8) = 0
g = {8, -15}
We can throw away the negative solution leaving us with:
g = 8 years old (age of girl)
.
age of boy:
g+7 = 8+7 = 15 years old (age of boy)