SOLUTION: Adding unity to the numerator as well as the denominator of a fraction makes it equal to 4/5. Subtracting 5 from each makes it equal to 1/2. What is the fraction?

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Question 910288: Adding unity to the numerator as well as the denominator of a fraction makes it equal to 4/5. Subtracting 5 from each makes it equal to 1/2. What is the fraction?
Found 2 solutions by stanbon, richwmiller:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Adding unity to the numerator as well as the denominator of a fraction makes it equal to 4/5. Subtracting 5 from each makes it equal to 1/2. What is the fraction?
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Equations::
(x+1)/(y+1) = 4/5
(x-1)/(y-1) = 1/2
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Cross-multiply to get:
5x+5 = 4y+4
2x-2 = y-1
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Rearrange::
5x - 4y = -1
2x - y = 1
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Modify for elimination::
5x - 4y = -1
8x - 4y = 4
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Subtract and solve for "x"::
3x = 5
x = 5/3
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Solve for "y"
2x-y = 1
10/3 - y = 1
y = 7/3
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Ans: # = (5/3)/(7/3) = 5/7
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Cheers,
Stan H.
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Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
(x+1)/(y+1) = 4/5,
(x-5)/(y-5) = 1/2
5*(x+1)=4*(y+1)
5x+5=4y+4
(x-5)/(y-5) = 1/2
2*(x-5)=(y-5)
2x-10=y-5
2x=y+5
y=2x-5
5x+5=4y+4
5x+5=4(2x-5)+4
5x+5=8x-20+4
5x+5=8x-16
3x=21
x = 7
y=2x-5
y-14-5
y = 9
7/9 is original fraction