SOLUTION: I am twice as old as you were when i was your age. When you are as old as I am, both our ages will add up to 27. How old am I?

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Question 526843: I am twice as old as you were when i was your age. When you are as old as I am, both our ages will add up to 27. How old am I?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = my age now
Let b = your age now
Note that the difference in our ages
will always be +a+-+b+
( I think I am older than you )
----------------------
given:
When my age was your age, then you
must have been +b+-+%28a-b%29+=+2b+-+a+
+a+=+2%2A%28+2b+-+a+%29+
+a+=+4b+-+2a+
+3a+=+4b+
(1) +b+=+%283%2F4%29%2Aa+
and
When your age becomes a, then I
will be +a+%2B+%28a-b%29+=+2a+-+b+
+a+%2B+2a+-+b+=+27+
(2) +3a+-+b+=+27+
Substitute (1) into (2)
(2) +3a+-+%283%2F4%29%2Aa+=+27+
(2) +12a+-+3a+=+108+
(2) +9a+=+108+
(2) +a+=+12+
I am 12
check:
(1) +b+=+%283%2F4%29%2Aa+
(1) +b+=+%283%2F4%29%2A12+
(1) +b+=+9+%7D%7D%0D%0A%282%29+%7B%7B%7B+3a+-+b+=+27+
(2) +3%2A12+-+9+=+27+
(2) +36+-+9+=+27+
(2) +27+=+27+
OK