SOLUTION: A boy's age is five-sixth of his sister's age. In eight years, the girl will be four times as old as her brother was five years ago. How old are they now?

Question 1013902: A boy's age is five-sixth of his sister's age. In eight years, the girl will be four times as old as her brother was five years ago. How old are they now?
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Call their ages NOW, b and s. Thus we have
b = (5/6)s or s = (6/5)b
In eight years she will be s + 8 and five years ago he was b - 5. So we have
s + 8 = 4(b - 5)
Substituting we get
(6/5)b + 8 = 4b - 20
Now subtract (6/5)b and add 20 to each side and get
(14/5)b = 28
Now multiply by 5/14 and
b = 10 so that
s = 12
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