SOLUTION: the numerator of a fraction exceeds the denominator by 3. if 3 is added to the numerator and 3 is subtracted from the denominator, the resulting fraction is equal to 5/2. find th

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Question 501962: the numerator of a fraction exceeds the denominator by 3. if 3 is added to the numerator and 3 is subtracted from the denominator, the resulting fraction is equal to 5/2. find the original fraction
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the numerator = a
Let the denominator = b
The original fraction is +a%2Fb+
given:
(1) +a+=+b+%2B+3+
(2) +%28+a+%2B+3+%29+%2F+%28+b+-+3+%29+=+5%2F2+
----------------------
(2) +a+%2B+3+=+%285%2F2%29%2A%28+b+-+3+%29+
(2) +2%2A%28+a+%2B+3+%29+=+5%2A%28+b+-+3+%29+
(2) +2a+%2B+6+=+5b+-+15+
(2) +2a+-+5b+=+-21+
and
(1) +a+-+b+=+3+
Multiply both sides of (1) by 2
and subtract (1) from (2)
(2) +2a+-+5b+=+-21+
(1) -2a+%2B+2b+=+-6+%7D%7D%0D%0A%7B%7B%7B+-3b+=+-27+
+b+=+9+
and, since
(1) +a+=+b+%2B+3+
(1) +a+=+9+%2B+3+
(1) +a+=+12+
The faction is +a%2Fb+=+12%2F9+