SOLUTION: raymund is half the age of his brother. five years ago, raymund was one-third the age of his brother. what is the present age of raymund?

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Question 1074092: raymund is half the age of his brother. five years ago, raymund was one-third the age of his brother. what is the present age of raymund?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Raymond's age now
Let +b+ = his brother's age now
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(1) +a+=+%281%2F2%29%2Ab+
(2) +a+-+5+=+%281%2F3%29%2A%28+b+-+5+%29+
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Substitute (1) into (2)
(2) +%281%2F2%29%2Ab+-+5+=+%281%2F3%29%2A%28+b+-+5+%29+
Multiply both sides by +6+
(2) +3b+-+30+=+2%2A%28+b+-+5+%29+
(2) +3b+-+30+=+2b+-+10+
(2) +b+=+20+
and
(1) +a+=+%281%2F2%29%2Ab+
(1) +a+=+%281%2F2%29%2A20+
(1) +a+=+10+
Raymond is 10 now
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check:
(2) +a+-+5+=+%281%2F3%29%2A%28+b+-+5+%29+
(2) +10+-+5+=+%281%2F3%29%2A%28+20+-+5+%29+
(2) +5+=+%281%2F3%29%2A15+
(2) +5+=+5+
OK