SOLUTION: If 5 is added to the numerator and the denominator of a fraction the value of the result is 5/7. If 5 is subtracted from the numerator and the denominator of the fraction the value

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Question 777864: If 5 is added to the numerator and the denominator of a fraction the value of the result is 5/7. If 5 is subtracted from the numerator and the denominator of the fraction the value of the result is 5/9. What is the fraction?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let the fraction be x/y

%28x%2B5%29%2F%28y%2B5%29+=5%2F7
cross multiply
7(x+5)=5(y+5)
7x+35=5y+25
7x-5y=-10..........................(1)

%28x-5%29%2F%28y-5%29+=5%2F9

9(x-5)=5(y-5)
9x-45=5y-25
9x-5y=20............................(2)
7 x -5 y = -10 .............1

9 x -5 y = 20 .............2
Eliminate y
multiply (1)by -1
Multiply (2) by 1
-7 x 5 y = 10
9 x -5 y = 20
Add the two equations
2 x = 30
/ 2
x = 15
plug value of x in (1)
7 x -5 y = -10
105 -5 y = -10
-5 y = -10 -105
-5 y = -115
y = 23
15/23