SOLUTION: The denominator of a fraction is 11 more than the numerator. If both the numerator and the denominator are decreased by 1 ​, the resulting fraction is equivalent to 3/14 . Find

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The denominator of a fraction is 11 more than the numerator. If both the numerator and the denominator are decreased by 1 ​, the resulting fraction is equivalent to 3/14 . Find       Log On


   

Question 1189319: The denominator of a fraction is 11 more than the numerator. If both the numerator and the denominator are decreased by 1 ​, the resulting fraction is equivalent to 3/14 . Find the fraction.
Thanks
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
The denominator of a fraction is 11 more than the numerator. If both the numerator and the denominator
are decreased by 1​, the resulting fraction is equivalent to 3/14. Find the fraction.
~~~~~~~~~~~~~~ 


The fraction is  x%2F%28x%2B11%29.


Modified fraction is  %28x-1%29%2F%28x%2B10%29.


An equation is  %28x-1%29%2F%28x%2B10%29 = 3%2F14.


Simplify and find x


    14(x-1)  = 3(x+10)

    14x - 14 = 3x + 30

      11x   = 44

        x   = 44/11 = 4

The fraction is  4%2F15.    ANSWER

Solved.



Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
The first fraction, x%2F%28x%2B11%29

The changed fraction, %28x-1%29%2F%28x%2B10%29

The changed fraction is equal to 3%2F14.

%28x-1%29%2F%28x%2B10%29=3%2F14
14%28x-1%29=3%28x%2B10%29
14x-14=3x%2B30
11x=30%2B14
11x=44
highlight%28x=4%29

The first fraction was highlight%284%2F15%29