SOLUTION: If the numerator and denominator of a fraction are both decreased by one the fraction becomes 2/3. If the numerator and denominator are both increased by one the fraction becomes 3

Question 437846: If the numerator and denominator of a fraction are both decreased by one the fraction becomes 2/3. If the numerator and denominator are both increased by one the fraction becomes 3/4. Find the original fraction
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If the numerator and denominator of a fraction are both decreased by one the fraction becomes 2/3. If the numerator and denominator are both increased by one the fraction becomes 3/4. Find the original fraction
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Let the fraction be x/y
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Equations:
(x-1)/(y-1) = 2/3
(x+1)/(y+1) = 3/4
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Rearrange:
3x-3=2y-2
4x+4=3y+3
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Rearrange:
3x - 2y = 1
4x - 3y = -1
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Multiply 1st by 3
Multiply 2nd by 2
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9x - 6y = 2
8x - 6y = -2
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Subtract and solve for "x":
x = 4
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solve for "y":
3x-2y = 1
12-2y = 1
2y = 11
y = 11/2
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Solution: (11/2,4)
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Cheers,
Stan H.
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