SOLUTION: tom is 4 years older than jerry. in 2 years, jerry will be halfas old as tom. find their ages now

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Question 431139: tom is 4 years older than jerry. in 2 years, jerry will be halfas old as tom. find their ages now
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let t = Tom's age now
Let j = Jerry's age now
given:
(1) +t+=+j+%2B+4+
(2) +j+%2B+2+=+%281%2F2%29%2A%28t+%2B+2%29+
-----------------------
(2) 2%2A%28+j+%2B+2+%29+=+t+%2B+2+
(2) +2j+%2B+4+=+t+%2B+2+
(2) +t+-+2j+=+2+
and
(1) +t+-+j+=+4+
Multiply both sides of (1) by 2
and subtract (2) from (1)
(1) +2t+-+2j+=+8+
(2) +-t+%2B+2j+=+-2+
+t+=+6+
Plug this into (1)
(1) +6+-+j+=+4+
+-j+=+-2+
+j+=+2+
Tom is 6 and Jerry is 2
check:
(1) +t+=+j+%2B+4+
(1) 6+=+2+%2B+4
OK
(2) +j+%2B+2+=+%281%2F2%29%2A%28t+%2B+2%29+
(2) +2+%2B+2+=+%281%2F2%29%2A%286+%2B+2%29+
(2) +4+=+%281%2F2%29%2A8+
(2) +8+=+8+
OK