SOLUTION: The value of 7 times a fraction's denominator is added to both the numerator and the denominator, and the result is subtracted from the original fraction. If the difference is 8, f

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: The value of 7 times a fraction's denominator is added to both the numerator and the denominator, and the result is subtracted from the original fraction. If the difference is 8, f      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 585564: The value of 7 times a fraction's denominator is added to both the numerator and the denominator, and the result is subtracted from the original fraction. If the difference is 8, find the original fraction.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The value of 7 times a fraction's denominator is added to both the numerator and the denominator, and the result is subtracted from the original fraction.
If the difference is 8, find the original fraction.
:
n%2Fd - %28%28n%2B7d%29%29%2F%28%28d%2B7d%29%29 = 8
;
n%2Fd - %28%28n%2B7d%29%29%2F%28%288d%29%29 = 8
multiply by 8d
8n - (n + 7d) = 8d*8
:
8n - n - 7d = 64d
7n - 7d = 64d
7n = 64d + 7d
7n = 71d
n = 71%2F7d
Only integer solution, d = 7 or a multiple of 7
Anyway, let's say
n = 71
d = 7
:
71%2F7 is the original fraction
:
See if that checks out, 7d = 49
71%2F7 - %28%2871%2B49%29%29%2F%28%287%2B49%29%29 =
71%2F7 - 120%2F56 =
568%2F56 - 120%2F56 = 448%2F56 = 8