SOLUTION: A girl is five years older than a boy. Nine years ago, the boy's age was two thirds the girl's age. The boy's age is...?

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Question 826957: A girl is five years older than a boy. Nine years ago, the boy's age was two thirds the girl's age. The boy's age is...?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +g+ = the girl's age now
Let +b+ = the boy's age now
-----------------
(1) +g+=+b+%2B+5+
(2) +b+-+9+=+%282%2F3%29%2A%28+g+-+9+%29+
--------------------------
(2) +3%2A%28+b+-+9+%29+=+2%2A%28+g+-+9+%29+
(2) +3b+-+27+=+2g+-+18+
(2) +3b+-+2g+=+9+
and
(1) +-b+%2B+g+=+5+
-------------------
Multiply both sides of (1) by 2
and add the equations
(2) +3b+-+2g+=+9+
(1) +-2b+%2B+2g+=+10+
+b+=+19+
and, since
(1) +g+=+b+%2B+5+
(1) +g+=+19+%2B+5+
(1) +g+=+24+
The boys age is 19
check:
(2) +b+-+9+=+%282%2F3%29%2A%28+g+-+9+%29+
(2) +19+-+9+=+%282%2F3%29%2A%28+24+-+9+%29+
(2) +10+=+%282%2F3%29%2A15+
(2) +10+=+10+
OK