SOLUTION: If 2 is added to the numerator of a fraction, the resulting fraction is 2/3. If 1 is subtracted from the denominator, the resulting fraction is 1/2. What is the original fraction?

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Question 412244: If 2 is added to the numerator of a fraction, the resulting fraction is 2/3. If 1 is subtracted from the denominator, the resulting fraction is 1/2. What is the original fraction?
Answer by mananth(16946) About Me  (Show Source):
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If 2 is added to the numerator of a fraction, the resulting fraction is 2/3. If 1 is subtracted from the denominator, the resulting fraction is 1/2. What is the original fraction?
let x be in the numerator
y denominator
x/y fraction
x+2/y = 2/3
cross multiply
3(x+2)=2y
3x+6=2y
3x-2y=-6........1
...
x/(y-1)=1/2
cross multiply
2x=y-1
2x-y=-1..........2
multiply (2) by -2
-4x+2y=+2
add to (1)
-x=-4
x=4 numerator
plug value ofy in (2)
y=9
4/9 is the fraction