SOLUTION: If the numerator of a fraction is decreased by 1 its values become 2/3, but if the denominator is increased by 5 its values become 1/2, what is the fraction

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: If the numerator of a fraction is decreased by 1 its values become 2/3, but if the denominator is increased by 5 its values become 1/2, what is the fraction      Log On


   

Question 1033107: If the numerator of a fraction is decreased by 1 its values become 2/3, but if the denominator is increased by 5 its values become 1/2, what is the fraction
Found 2 solutions by robertb, josgarithmetic:
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let the fraction be x/y.
The first part of the problem says that %28x-1%29%2Fy+=+2%2F3, while the second part says that x%2F%28y%2B5%29+=+1%2F2.
The second equation is equivalent to x+=+%281%2F2%29%28y%2B5%29.
Upon substitution into the first equation, we get %28%281%2F2%29%28y%2B5%29-1%29%2Fy+=+2%2F3
<==> %281%2F2%29y%2B5%2F2+-+1+=+%282%2F3%29y
==> y%2F2+%2B3%2F2+=+%282%2F3%29y
==> 3%2F2+=+%281%2F6%29y
==> y = 9.
==> x = 7.
==> the fraction is 7/9.

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
system%28%28n-1%29%2Fd=2%2F3%2Cn%2F%28d%2B5%29=1%2F2%29

The system appears like rational equations but .....

system%28n-1=2d%2F3%2C2n=d%2B5%29, with a little help from Multiplication Property of Equality. How to go further is up to you.


system%283n-3=2d%2C2n-d=5%29

system%283n-2d=3%2C2n-d=5%29

Multiplying second equation by -2 gives system%283n-2d=3%2C-4n%2B2d=-10%29 allowing now easy use of Elimination Method (setup now for it).

highlight_green%28%283n-2d%29%2B%28-4n%2B2d%29=3%2B%28-10%29%29----------You finish this...