SOLUTION: the numerator of a fraction is 8 less than the denominator. If 1 is added to the numerator and subtracted from the denominator, the resulting fraction is 2/3. Find the fraction

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Question 354657: the numerator of a fraction is 8 less than the denominator. If 1 is added to the numerator and subtracted from the denominator, the resulting fraction is 2/3. Find the fraction
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
HI,
let n represent the value of the denominator, then (n -8) would be the numerator
.
question states*
%28%28n-8%29+%2B+1%29%2F%28n-1%29=+%282%2F3%29
.
%28n+-7%29%2F%28n-1%29+=+%282%2F3%29
.
cross multiply to solve
2%2A%28n-1%29+=+3%2A%28n-7%29
.
simplify
2n-+2=+3n+-+21
.
19+=+n
fraction is ( 11/19)
.
check your answer
%2812%29%2F%2818%29+=+%282%2F3%29