SOLUTION: a fraction reduces of 1/4 when two is subtracted from the numerator and three is added to be the denominator. but it reduces to 2/3. if six is added to the numerator and the denomi

Question 257459: a fraction reduces of 1/4 when two is subtracted from the numerator and three is added to be the denominator. but it reduces to 2/3. if six is added to the numerator and the denominator is multiplied by three. find the fraction.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
a fraction reduces to 1/4 when two is subtracted from the numerator and three is added to be the denominator.
but it reduces to 2/3 if six is added to the numerator and the denominator is multiplied by three. find the fraction.
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Equations:
Let the fraction be x/y
------------
(x-2)/(y+3) = 1/4
--
(x+6)/(3y) = 2/3
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Simplify :
4x-8= y+3
3x+18 = 6y
--------------------------
Rearrange:
4x-y = 11
3x-6y = -18
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Multiply 1st by 6 to get:
24x-6y = 66
3x-6y = -18
------
Subtract 2nd from 1st to get:
21x = 84
x = 4
-----
Substitute into 4x-y=11 to solve for "y":
4*4-y = 11
y = 5
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The fraction is 4/5
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Cheers,
Stan H.
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