SOLUTION: Fred is ten years younger than John. Two years ago, Fred was one-half of John's age. How old is each?

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Question 1053592: Fred is ten years younger than John. Two years ago, Fred was one-half of John's age. How old is each?
Found 2 solutions by josmiceli, Alan3354:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Fred's age now
Let +b+ = John's age now
----------------------------
(1) +a+=+b+-+10+
(2) +a+-+2+=+%281%2F2%29%2A%28+b+-+2+%29+
----------------------------
Substitute (1) into (2)
(2) +b+-+10+-+2+=+%281%2F2%29%2A%28+b+-+2+%29+
(2) +b+-+12+=+%281%2F2%29%2A%28+b+-+2+%29+
(2) +2%2A%28+b+-+12+%29+=+b+-+2+
(2) +2b+-+24+=+b+-+2+
(2) +b+=+24+-+2+
(2) +b+=+22+
and
(1) +a+=+b+-+10+
(1) +a+=+22+-+10+
(1) +a+=+12+
------------------
Fred is 12
John is 22
---------------
check:
(2) +a+-+2+=+%281%2F2%29%2A%28+b+-+2+%29+
(2) +12+-+2+=+%281%2F2%29%2A%28+22+-+2+%29+
(2) +10+=+%281%2F2%29%2A20+
92) +10+=+10+
OK

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Fred is ten years younger than John. Two years ago, Fred was one-half of John's age. How old is each?
------------
Two years ago, Fred was one-half of John's age, AND he was 10 years younger.
--> 10 & 20 two years ago.
etc.