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

Algebra ->  Percentage-and-ratio-word-problems -> 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      Log On


   

Question 121719: 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. Find the original fraction.
Answer by stanbon(75887) About Me  (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. Find the original fraction.
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Starting:
Let the numerator be 4x; Then the denominator is 5x
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Modifying to get EQUATION:
(4x-5)/(5x+4) = 1/2
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Cross-multiply to solve for x:
2(4x-5) = 5x+4
8x-10 = 5x+4
3x=14
x = 14/3
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Original fraction:
[4(14/3)]/[5(14/3) = [56/3]/[70/3] = 56/70
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Cheers,
Stan Hanson