SOLUTION: The denominator of a fraction is 7 more than the numerator. If both the numerator and the denominator are decreased by 2​, the resulting fraction is equivalent to 6/13. Find th

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Question 1204643: The denominator of a fraction is 7 more than the numerator. If both the numerator and the denominator are decreased by 2​, the resulting fraction is equivalent to
6/13. Find the fraction.
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
n%2F%28n%2B7%29 original fraction

%28n-2%29%2F%28n%2B5%29=6%2F13
.
.

highlight%288%2F15%29

Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
.
The denominator of a fraction is 7 more than the numerator. If both the numerator and the denominator
are decreased by 2​, the resulting fraction is equivalent to 6/13. Find the fraction.
~~~~~~~~~~~~~~~~~~~~~~~ 

Let x be the numerator of the original fraction.
Then the denominator is (x+7).


From the condition, we have this equation

    %28x-2%29%2F%28%28x%2B7%29-2%29 = 6%2F13.


Simplify and find x

    %28x-2%29%2F%28x%2B5%29 = 6%2F13

    13(x-2) = 6(x+5)

    13x - 26 = 6x + 30

    13x - 6x = 30 + 26

        7x   =   56.

         x   =   56/7 = 8.


ANSWER.  The fraction is  8%2F15.

Solved.



Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The denominator is 7 more than the numerator.

When both numerator and denominator are decreased by 2, the denominator is again 7 more than the numerator.

The fraction after the numerator and denominator are both decreased by 2 is equivalent to 6/13 -- a fraction in which the denominator is 7 more than the numerator.

So increase the numerator and denominator of the fraction 6/13 by 2 to find that the original fraction is 8/15.

ANSWER: 8/15