SOLUTION: The value of a fraction is 2/3. If the numerator is increased by 14 and the denominator is decreased by 9 the value of the resulting fraction will be the reciprocal of the value of

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The value of a fraction is 2/3. If the numerator is increased by 14 and the denominator is decreased by 9 the value of the resulting fraction will be the reciprocal of the value of      Log On


   

Question 739476: The value of a fraction is 2/3. If the numerator is increased by 14 and the denominator is decreased by 9 the value of the resulting fraction will be the reciprocal of the value of the original fraction. What is the original fraction?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Let numerator be n
Let denominator be d.
n%2Fd+=+2%2F3.

The longer part of the description gives %28n%2B14%29%2F%28d-9%29=d%2Fn.

Working with the longer equation,+n%28n%2B14%29=d%28d-9%29
n%5E2%2B14n=d%5E2-9d.

Using the 2/3 equation, n=2d%2F3, so try substituting:
d%5E2-9d=4d%5E2%2F9%2B14%2A2d%2F3
Multiply both sides by 9
9d%5E2-81d=4d%5E2%2B84d

5d%5E2-165d=0
d%5E2-33d=0
d%28d-33%29=0
... highlight%28d=33%29
meaning highlight%28n=22%29.