SOLUTION: I am three times as old as my brother. Five years later I shall be two and a half times as old as my brother. How old am I and how old is my brother?

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Question 1098043: I am three times as old as my brother. Five years later I shall be two and a half times as old as my brother. How old am I and how old is my brother?
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
system%28m=3b%2Cm%2B5=%285%2F2%29%28b%2B5%29%29

2m%2B10=5b%2B25
2m=5b%2B15
2%283b%29=5b%2B15
6b=5b%2B15
highlight%28b=15%29-----------Brother is 15.
-
highlight%2845%29-----------Other person's age, 45.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = my age now
Let +b+ = my brother's age now
------------------------------------
(1) +a+=+3b+
(2) +a+%2B+5+=+%285%2F2%29%2A%28+b+%2B+5+%29+
------------------------------
Multiply both sides of (2) by +2+
(2) +2a+%2B+10+=+5b+%2B+25+
(2) +2a+-+5b+=+15+
Plug (1) into (2)
(2) +2%2A%28+3b+%29+-+5b+=+15+
(2) +6b+-+5b+=+15+
(2) +b+=+15+
and
(1) +a+=+3b+
(1) +a+=+3%2A15+
(1) +a+=+45+
--------------------
I an 45 and my brother is 15
------------------------------
check:
I am 3 times as old as my brother TRUE
(2) +a+%2B+5+=+%285%2F2%29%2A%28+b+%2B+5+%29+
(2) +45+%2B+5+=+%285%2F2%29%2A%28+15+%2B+5+%29+
(2) +50+=+%285%2F2%29%2A20+
(2) +50%2F20+=+5%2F2+
(2) +5%2F2+=+5%2F2+
OK