if 1 is added to the numerator and 3 to the denominator of a fraction it becomes 1/2 if 1 is subtracted from the numenator and 2 is added to the denominator it becomes 2/5 find the fractions
originial fraction ---- a/b
case 1:
(a+1)/(b+3) = 1/2
2a +2 = b+3 ----> 2a - b = 1 or b = 2a-1
case 2:
(a-1)/(b+2) = 2/5
5a - 5 = 2b+4
5a - 2b = 9
use substitution:
5a - 2(2a-1) = 9
a = 7 , then b = 13
the original fraction was 7/13