SOLUTION: I could really use some help with this: "The sum of the numerator and denominator of a fraction is 40. If 3 is added to the numerator, and 2 added to the denominator, the new f

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: I could really use some help with this: "The sum of the numerator and denominator of a fraction is 40. If 3 is added to the numerator, and 2 added to the denominator, the new f      Log On


   

Question 404979: I could really use some help with this:
"The sum of the numerator and denominator of a fraction is 40. If 3 is added to the numerator, and 2 added to the denominator, the new fraction is equal to 4/5.
What is the original fraction? "
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the numerator and denominator of a fraction is 40. If 3 is added to the numerator, and 2 added to the denominator, the new fraction is equal to 4/5.
What is the original fraction? "
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Let the original fraction be x/y.
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Equations:
x + y = 40
(x+3)/(y+2) = 4/5
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Modify the 2nd equation as follows:
5(x+3) = 4(y+2)
5x+15 = 4y+8
5x-4y = -7
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Now, solve the system:
x+y = 40
5x-4y = -7
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Multiply the 1st equation by 5:
5x + 5y = 5*40
5x-4y = -7
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Subtract the bottom eq. from the top and solve for "y":
9y = 207
y = 23
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Solve for "x":
x + y = 40
x + 23 = 40
x = 17
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Original Fraction: 17/23
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Cheers,
Stan H.
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