SOLUTION: The numerator of a fraction is 3 less than the denominator. If 5 is added to both the numerator and denominator, the value resulting fraction is 3/4. Find the original fraction

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The numerator of a fraction is 3 less than the denominator. If 5 is added to both the numerator and denominator, the value resulting fraction is 3/4. Find the original fraction      Log On


   

Question 677041: The numerator of a fraction is 3 less than the denominator. If 5 is added to both the numerator and denominator, the value resulting fraction is 3/4. Find the original fraction
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the fraction = +a%2Fb+
given:
(1) +a+=+b+-+3+
(2) +%28+a+%2B+5+%29+%2F+%28+b+%2B+5+%29+=+3%2F4+
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Substitute (1) into (2)
(2) +%28+b+-+3+%2B+5+%29+%2F+%28+b+%2B+5+%29+=+3%2F4+
(2) +%28+b+%2B+2+%29+%2F+%28+b+%2B+5+%29+=+3%2F4+
Multiply both sides by +4%2A%28+b-5+%29+
(2) +4%2A%28+b+%2B+2+%29+=+3%2A%28+b+%2B+5+%29+
(2) +4b+%2B+8+=+3b+%2B+15+
(2) +b+=+7+
and, since
(1) +a+=+b+-+3+
(1) +a+=+7+-+3+
(1) +a+=+4+
The fraction is +a%2Fb+=+4%2F7+
check answer:
(2) +%28+a+%2B+5+%29+%2F+%28+b+%2B+5+%29+=+3%2F4+
(2) +%28+4+%2B+5+%29+%2F+%28+7+%2B+5+%29+=+3%2F4+
(2) +9+%2F+12+=+3%2F4+
(2) +3%2F4+=+3%2F4+
OK