Question 687224
 The ratio of the numerator to the denominator of a certain fraction is five to eight. If five is subtracted from the numerator and four is added to the denominator, the new fraction reduces to one-half. What is the original fraction?

let numerator be x and denominator be y
x/y = 5/8
y= 8x/5

If five is subtracted from the numerator and four is added to the denominator, the new fraction reduces to one-half. 

(x-5)/(y+4) =1/2

2(x-5)=(y+4)

2x-10= y+4
2x-y = 14

2x- (8x/5)=14

multiply by 10

20x -16x = 140
4x=140
x=35
y=56

 the original fraction is 35/56