SOLUTION: John was twice as old as bob last year. In seven years john will be half again as bob. how old are they now?

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Question 476970: John was twice as old as bob last year. In seven years john will be half again as bob. how old are they now?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let j = John's age now
Let b = Bob's age now
given:
(1) +j+-+1+=+2%2A%28+b+-+1+%29+
(2) +j+%2B+7+=+1.5%2A%28+b+%2B+7+%29+
Note that "half again" means 1.5 times
---------------------------------
(1) +j+-+1+=+2%2A%28+b+-+1+%29+
(1) +j+-+1+=+2b+-+2+
(1) +2b+-+j+=+1+
and
(2) +j+%2B+7+=+1.5%2A%28+b+%2B+7+%29+
(2) +j+%2B+7+=+1.5b+%2B+10.5+
(2) +-1.5b+%2B+j+=+3.5+
--------------------------
Add (1) and (2)
(1) +2b+-+j+=+1+
(2) +-1.5b+%2B+j+=+3.5+
+.5b+=+4.5+
+b+=+9+
Plug this result back into (1)
(1) +2b+-+j+=+1+
(1) +2%2A9+-+j+=+1+
(1) +j+=+18+-+1+
(1) +j+=+17+
John is 17 now and Bob is 9 now
check:
(2) +j+%2B+7+=+1.5%2A%28+b+%2B+7+%29+
(2) +17+%2B+7+=+1.5%2A%28+9+%2B+7+%29+
(2) +24+=+1.5%2A16+
(2) +24+=+24+
OK