SOLUTION: Gary is today 5 times as old as Joan. Two years later, he will be 4 times as old as Joan. How old is Joan today?

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Question 760574: Gary is today 5 times as old as Joan. Two years later, he will be 4 times as old as Joan. How old is Joan today?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +g+ = Gary's age now
Let +j+ = Joan's age now
+g+%2B+2+ = Gary's age in 2 years
+j+%2B+2+ = Joan's age in 2 years
----------------------------
(1) +g+=+5j+
(2) +g+%2B+2+=+4%2A%28+j+%2B+2+%29+
-----------------------
(2) +g+%2B+2+=+4j+%2B+8+
(2) +g+=+4j+%2B+6+
By substitution:
(2) +5j+=+4j+%2B+6+
(2) +j+=+6+
and, since
(1) +g+=+5j+
(1) +g+=+5%2A6+
(1) +g+=+30+
Joan is 6 years old
check:
(2) +g+%2B+2+=+4%2A%28+j+%2B+2+%29+
(2) +30+%2B+2+=+4%2A%28+6+%2B+2+%29+
(2) +32+=+4%2A8+
(2) +32+=+32+
OK