SOLUTION: A fraction is equivalent to 2/5. if the numerator of the fraction is decreased by 2 and its denominator is increased by 1, then the resulting fraction is equivalent to 1/4. what is

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Question 69466: A fraction is equivalent to 2/5. if the numerator of the fraction is decreased by 2 and its denominator is increased by 1, then the resulting fraction is equivalent to 1/4. what is the value of the numerator of the original fraction? (plz. and thank you:)
Answer by stanbon(75887) (Show Source):
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A fraction is equivalent to 2/5. if the numerator of the fraction is decreased by 2 and its denominator is increased by 1, then the resulting fraction is equivalent to 1/4. what is the value of the numerator of the original fraction?
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x/y=2/5 or 5x=2y or 5x-2y=0
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If you make the changes you get:
(x-2)/(y+1)=1/4
4x-8 = y+1
4x-y=9
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So you have two equations and can solve for x and for y:
y=(5/2)x
Substitute that into the 2nd equation to solve for x:
4x-(5/2)x=9
1.5x=9
x=6
Substitute to solve for y:
y=(5/2)6=15
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x=6, y=15
Cheers,
Stan H.