Question 244861
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.