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Question 203140: The difference between the numerator and the denominator of a certain proper fraction is 24. If ⅜ is added to the numerator and ¼ subtracted from the denominator, the value of resulting fraction is 3⁄14. Find the numerator
and denominator.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The difference between the numerator and the denominator of a certain proper fraction is 24. If ⅜ is added to the numerator and ¼ subtracted from the denominator, the value of resulting fraction is 3⁄14. Find the numerator
and denominator.
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Numerator: x
Denominator: y
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Equations:
x - y = 24
[x+(3/8)]/[y-(3/14)]=3/14
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Rearrange the 2nd equation to get:
[(8x+3)/8]/[(14y-3)/14] = (3/14)
Invert the left side and multiply to get:
[14(8x+3)]/[8(14y-3)] = (3/14)
Cross-multiply to get:
[14^2(8x+3)] = [24(14y-3)]
Divide both sides by 24 to get:
(49/6)(8x+3) = 14y-3
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Substitute from the 1st equation (y=x-24) to get
(49/6)(8x+3) = 14(x-24)-3
(49/6)(8x+3) = 14x -339
49(8x+3) = 49(14x-339)
392x+147 = 686x-16611
16758 = 294x
x = 57 This is the numerator)
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Solve for "y":
y = 57-24
y = 33 (This is the denominator)
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Cheers,
Stan H.
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