SOLUTION: 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 fractio

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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?

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Found 3 solutions by mananth, ikleyn, greenestamps:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website!
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

Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website!
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Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

The other tutor showed a valid solution using two variables.

Setting the problem up using a single variable makes solving the problem much easier.

Given the information that the ratio of numerator to denominator is 5:8, let the numerator be 5x and the denominator be 8x. That is a very common way to set up a problem where the ratio of two numbers is given.

The fraction with 5 subtracted from the numerator and 4 added to the denominator is equivalent to 1/2:

The original fraction has numerator 5x=35 and denominator 8x=56.

ANSWER: 35/56