SOLUTION: Two years from now, Jim will be twice as old as Joe will be then. Ten years ago, Jim was five times as old as Joe was. Find the present ago of each

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Question 644306: Two years from now, Jim will be twice as old as Joe will be then. Ten years ago, Jim was five times as old as Joe was. Find the present ago of each
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Jim's age now
Let +b+ = Joe's age now
given:
(1) +a+%2B+2+=+2%2A%28+b+%2B+2+%29+
(2) +a+-+10+=+5%2A%28+b+-+10+%29+
----------------------
(1) +a+%2B+2+=+2b+%2B+4+
(1) +a+-+2b+=+2+
and
(2) +a+-+10+=+5b+-+50+
(2) +-a+%2B+5b+=+40+
------------------
Add the equations
+3b+=+42+
+b+=+14+
and, since
(1) +a+-+2%2A14+=+2+
(1) +a+-+28+=+2+
(1) +a+=+30+
Jim is 30 now
Joe is 14 now
check:
(2) +-a+%2B+5b+=+40+
(2) +-30+%2B+5%2A14+=+40+
(2) +-30+%2B+70+=+40+
(2) +40+=+40+
OK