SOLUTION: If you increase the numerator if by 3 and the denominator by 4, the value of the fraction will be doubled. The denominator of the original fraction is 1 more than the numerator. Fi
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Question 417652: If you increase the numerator if by 3 and the denominator by 4, the value of the fraction will be doubled. The denominator of the original fraction is 1 more than the numerator. Find the original fraction.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If you increase the numerator if by 3 and the denominator by 4, the value of the fraction will be doubled. The denominator of the original fraction is 1 more than the numerator. Find the original fraction.
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Let the original fraction be x/y
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Equations:
(x+3)/(y+4) = 2(x/y)
y = x+1
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Substitute for "y" and solve for "x":
(x+3)/(x+5) = 2(x/(x+1))
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Cross-multiply:
(x+3)(x+1) = (x+5)(2x)
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x^2+4x+3 = 2x^2+10x
x^2+6x-3 = 0
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x = [-6 +- sqrt(36-4*1*-3)]/2
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x = [-6 +- sqrt(48)]/2
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x = [-6 +- 4sqrt(3)]/2
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x = -3+2sqrt(3)
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Solve for "y":
y = x+1
y = -2+2sqrt(3)
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I doubt that is the answer you are looking for
but that is what your post implies.
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Cheers,
Stan H.
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