SOLUTION: George is 3 years older than his sister Janet. In 7 years she will be six-sevenths of his age. How old is George?

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Question 555415: George is 3 years older than his sister Janet. In 7 years she will be six-sevenths of his age. How old is George?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +g+ = George's age now
Let +j+ = Janet's age now
given:
(1) +g+=+j+%2B+3+
(2) +j+%2B+7+=+%286%2F7%29%2A%28+g+%2B+7+%29+
--------------------
(1) +j+=+g+-+3+
Substitute (1) into (2)
(2) +g+-+3+%2B+7+=+%286%2F7%29%2A%28+g+%2B+7+%29+
(2) +7%2A%28+g+%2B+4+%29+=+6%2A%28+g+%2B+7+%29+
(2) +7g+%2B+28+=+6g+%2B+42+
(2) +g+=+42+-+28+
(2) +g+=+14+
and, since
(1) +j+=+g+-+3+
(1) +j+=+14+-+3+
(1) +j+=+11+
George is 14
check answer
(2) +j+%2B+7+=+%286%2F7%29%2A%28+g+%2B+7+%29+
(2) +11+%2B+7+=+%286%2F7%29%2A%28+14+%2B+7+%29+
(2) +18+=+%286%2F7%29%2A21+
(2) +18%2A7+=+6%2A21+
(2) +126+=+126+
OK