SOLUTION: A brother is 3years older than his sister,5years ago,the ratio of their ages was 4:3.find their present ages

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Question 884192: A brother is 3years older than his sister,5years ago,the ratio of their ages was 4:3.find their present ages
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +b+ = brother's age now
Let +s+ = sister's age now
--------------------------
(1) +b+=+s+%2B+3+
(2) +%28+b++-+5+%29+%2F+%28+s+-+5+%29+=+4%2F3+
-----------------------------
(2) +3%2A%28+b+-+5+%29+=+4%2A%28+s+-+5+%29+
(2) +3b+-+15+=+4s+-+20+
(2) +3b+-+4s+=+-5+
and
(1) +b+-+s+=+3+
Multiply both sides of (1) by +3+
and subtract (2) from (1)
(1) +3b+-+3s+=+9+
(2) +-3b+%2B+4s+=+5+
---------------------
+s+=+14+
and, since
(1) +b+=+s+%2B+3+
(1) +b+=+14+%2B+3+
(1) +b+=+17+
The sister is 14 and the brother is 17
check:
(2) +%28+17++-+5+%29+%2F+%28+14+-+5+%29+=+4%2F3+
(2) +12+%2F+9+=+4%2F3+
(2) +4%2F3+=+4%2F3+
OK