SOLUTION: If 5 is added to both the numerator and the denominator of a fraction the resut is 4/7. If 1 is subtractedfrom both the numerator and denominator the resut is 2/5. Find the fractio

Algebra ->  Proportions  -> Lessons -> SOLUTION: If 5 is added to both the numerator and the denominator of a fraction the resut is 4/7. If 1 is subtractedfrom both the numerator and denominator the resut is 2/5. Find the fractio      Log On


   

Question 951408: If 5 is added to both the numerator and the denominator of a fraction the resut is 4/7. If 1 is subtractedfrom both the numerator and denominator the resut is 2/5. Find the fraction.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let the fraction be X%2FY
%28X%2B5%29%2F%28Y%2B5%29=4%2F7
4%28Y%2B5%29=7%28X%2B5%29
4Y%2B20=7X%2B35
1.-7X%2B4Y=15
.
.
%28X-1%29%2F%28Y-1%29=2%2F5
5%28X-1%29=2%28Y-1%29
5X-5=2Y-2
2.5X-2Y=3
Multiply eq. 2 by 2 and add to eq. 1,
-7X%2B4Y%2B10X-4Y=15%2B6
3X=21
X=7
So then,
5%287%29-2Y=3
35-2Y=3
-2Y=-32
Y=16