SOLUTION: If the numerator of a certain fraction is increased by 5 and the denominator is decreased by 1, the resulting fraction is 8/3. However, if the numerator of the original fraction i
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Question 204987: If the numerator of a certain fraction is increased by 5 and the denominator is decreased by 1, the resulting fraction is 8/3. However, if the numerator of the original fraction is doubled and the denominator is increased by 7, the resulting fraction is 6/11. Find the original fraction. Found 2 solutions by rfer, stanbon:Answer by rfer(16322) (Show Source):
You can put this solution on YOUR website! If the numerator of a certain fraction is increased by 5 and the denominator is decreased by 1, the resulting fraction is 8/3. However, if the numerator of the original fraction is doubled and the denominator is increased by 7, the resulting fraction is 6/11. Find the original fraction
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Let the original fraction be x/y.
Equations:
(x+5)/(y-1) = 8/3
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(2x)/(y+7)/ 6/11
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Rearrange:
3(x+5) = 8(y-1)
11(2x) = 6(y+7)
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Modify:
8y - 3x = 23
6y -22x = -42
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Set up for elimination:
48y - 18x = 6*23
48y -176x = 8*-42
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Subtract the 2nd equation from the 1st to solve for "x":
158x = 474
x = 3
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Substitute into 8y -3x = 23 to solve for "y":
8y -3*3 = 23
8y - 9 = 23
8y = 32
y = 4
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Original fraction: x/y = 3/4
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Cheers,
Stan H.
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