SOLUTION: The numerator of a fraction is 10 less than the denominator. If the numerator is increased by 5 and the denominator is decreased by 5.The fraction becomes 1. Find the fraction.

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Question 555651: The numerator of a fraction is 10 less than the denominator. If the numerator is increased by 5 and the denominator is decreased by 5.The fraction becomes 1. Find the fraction.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = numerator
Let +b+ = denominator
given:
(1) +a+=+b+-+10+
(2) +%28+a+%2B+5+%29+%2F+%28+b+-+5+%29+=+1+
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(2) +a+%2B+5+=+b+-+5+
(2) +b+-+a+=+10+
Also, from (1)
(1) +b+-+a+=+10+
----------------
It looks like the fraction can be anything
where +b+-+a+=+10+
suppose +b+=+7471+, then +a+=+7461+
+%28+7461+%2B+5+%29+%2F+%28+7471+-+5+%29+=+7466+%2F+7466+
This equals 1, so the fraction can be any
+a+%2F+%28+a+%2B+10+%29+