SOLUTION: A fraction becomes 1/2 if 1 is added to both numerator and dnominator and if 1 is subtracted from both its numerator and denominator ,it becomes 1/3 .Find the fraction.

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A fraction becomes 1/2 if 1 is added to both numerator and dnominator and if 1 is subtracted from both its numerator and denominator ,it becomes 1/3 .Find the fraction.      Log On


   

Question 1066694: A fraction becomes 1/2 if 1 is added to both numerator and dnominator and if 1 is subtracted from both its numerator and denominator ,it becomes 1/3 .Find the fraction.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
OK, let the fraction be A%2FB.
%28A%2B1%29%2F%28B%2B1%29=1%2F2
2%28A%2B1%29=B%2B1
2A%2B2=B%2B1
1.2A-B=-1
and
%28A-1%29%2F%28B-1%29=1%2F3
3%28A-1%29=B-1
3A-3=B-1
2.3A-B=2
Subtracting 1 from 2,
3A-B-%282A-B%29=2-%28-1%29
3A-B-2A%2BB=2%2B1
A=3
So then,
2%283%29-B=-1
6-B=-1
B=6%2B1
B=7