SOLUTION: If 5 is added both to the numerator and denominator of a fraction, the result is equivalent to 3/4. If 3 is subtracted from both numerator and denominator of the original fraction,

Algebra ->  Proportions -> SOLUTION: If 5 is added both to the numerator and denominator of a fraction, the result is equivalent to 3/4. If 3 is subtracted from both numerator and denominator of the original fraction,      Log On


   

Question 824357: If 5 is added both to the numerator and denominator of a fraction, the result is equivalent to 3/4. If 3 is subtracted from both numerator and denominator of the original fraction, the new result is equivalent to 1/4. Find the orginal fraction.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the original fraction = +a%2Fb+
given:
(1) +%28+a+%2B+5+%29+%2F+%28+b+%2B+5+%29+=+3%2F4+
and
(2) +%28+a+-+3+%29+%2F+%28+b+-+3+%29+=+1%2F4+
----------------------------
Multiply both sides of (1) by +4%2A%28+b+%2B+5+%29+
(1) +4%2A%28+a%2B5+%29+=+3%2A%28+b%2B5+%29+
(1) +4a+%2B+20+=+3b+%2B+15+
(1) +3b+-+4a+=+5+
------------------
Multiply both sides of (2) by +4%2A%28+b-3+%29+
(2) +4%2A%28+a-3+%29+=+b+-+3+
(2) +4a+-+12+=+b+-+3+
(2) +-b+%2B+4a+=+9+
Add (1) and (2)
(1) +3b+-+4a+=+5+
(2) +-b+%2B+4a+=+9+
+2b+=+14+
+b+=+7+
and, since
(1) +3b+-+4a+=+5+
(1) +3%2A7+-+4a+=+5+
(1) +4a+=+21+-+5+
(1) +4a+=+16+
(1) +a+=+4+
------------
+a%2Fb+=+4%2F7+
The original fraction is 4/7
check:
(2) +-b+%2B+4a+=+9+
(2) +-7+%2B+4%2A4+=+9+
(2) +-7+%2B+16+=+9+
(2) +9+=+9+
OK