SOLUTION: A rational number becomes 2 / 3 when 1 is added to its numerator and the denominator. But becomes 3 / 2 if 4 is subtracted from each one of the numerator and denominator. Find the

Algebra ->  Linear-equations -> SOLUTION: A rational number becomes 2 / 3 when 1 is added to its numerator and the denominator. But becomes 3 / 2 if 4 is subtracted from each one of the numerator and denominator. Find the       Log On


   

Question 1080972: A rational number becomes 2 / 3 when 1 is added to its numerator and the denominator. But becomes 3 / 2 if 4 is subtracted from each one of the numerator and denominator. Find the rational number
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
%28n%2B1%29%2F%28d%2B1%29=2%2F3
2%28d%2B1%29=3%28n%2B1%29
2d%2B2=3n%2B3
2d-3n=1
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%28n-4%29%2F%28d-4%29=3%2F2
2%28n-4%29=3%28d-4%29
2n-8=3d-12
3d-12=2n-8
3d-2n=-8%2B12
3d-2n=4
-
system%282d-3n=1%2C3d-2n=4%29
-
%282d-3n%29%2B%283d-2n%29=1%2B4
5d-5n=5
d-n=1
-

2d-3n=1
2%28n%2B1%29-3n=1
2n%2B2-3n=1
-n%2B2=1
n-2=-1
n=-1%2B2
highlight%28n=1%29
highlight%28d=2%29%29

Rational Number: highlight%28highlight%281%2F2%29%29