SOLUTION: Five years ago a girl was one-half as old as her brother was then,and now she is three years younger than he is.Find their present ages.

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Question 244861: Five years ago a girl was one-half as old as her brother was then,and now she is three years younger than he is.Find their present ages.
Answer by dabanfield(803) About Me  (Show Source):
You can put this solution on YOUR website!
Let B represent the boy's current age and G the girl's current age:
We know that now the girl is 3 years younger than the boy so:
G = B - 3
Five years ago the ages were B - 5 and G -5. We know that back then the girl's age was half the boy's so:
(B-5)/2 = (G-5) or
(B-5) = 2*(G-5)
Substituting B-3 for G in the equation above we have:
(B-5) = 2*((B-3)-5)
B-5 = (2*B) - 6 - 10
Simplifying we have:
-5+16 = (2*B) - B
11 = B
Substituting B = 11 in the current ages equation, B = G-3, we have 11 = G -3 or G = 8.
The Boy is 11 and the girl is 8.