SOLUTION: Four years ago, Jane was twice as old as Sam. Four years on from now, Sam will be ¾ of Jane's age. How old is Jane now?

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Question 993937: Four years ago, Jane was twice as old as Sam. Four years on from now, Sam will be ¾ of Jane's age. How old is Jane now?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +j+ = Jane's age now
Let +s+ = Sam's age now
(1) +j+-+4+=+2%2A%28+s+-+4+%29+
(2) +s+%2B+4+=+%283%2F4%29%2A%28+j+%2B+4+%29+
-------------------------
(1) +j+-+4+=+2s+-+8+
(1) +2s+-+j+=+4+
-------------------
(2) +4s+%2B+16+=+3j+%2B+12+
(2) +-4s+%2B+3j+=+4+
----------------------
Multiply both sides of (1) by +3+
and add the equations
(1) +6s+-+3j+=+12+
(2) +-4s+%2B+3j+=+4+
--------------------
+2s+=+16+
+s+=+8+
and
(1) +j+-+4+=+2%2A%28+8+-+4+%29+
(1) +j+=+2%2A4+%2B+4+
(1) +j+=+12+
Jane is 12 now
---------------
check:
4 yrs ago, Jane was 8
4 yrs ago, Sam was 4
Jane was 2X as old
------------------
In 4 yrs, Sam is 12
In 4 yrs, Jane is 16
+%283%2F4%29%2A16+=+12+
OK