SOLUTION: The numerator of a fraction is 4 less than its denominator, if 3 is added both the numerator and denominator, the resulting number is 3/4. what is the original fraction. Explain.

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Question 1202448: The numerator of a fraction is 4 less than its denominator, if 3 is added both the numerator and denominator, the resulting number is 3/4. what is the original fraction. Explain.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52809) About Me  (Show Source):
You can put this solution on YOUR website!
.
The numerator of a fraction is 4 less than its denominator,
if 3 is added both the numerator and denominator, the resulting number is 3/4.
what is the original fraction. Explain.
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Let x be the denominator.
Then the numerator is (x-4), according to the problem.


So, the original fraction is  %28x-4%29%2Fx.


After adding 3 to both the numerator and denominator, the fraction is  

    %28%28x-4%29%2B3%29%2F%28x%2B3%29 = %28x-1%29%2F%28x%2B3%29.


It is equal to 3%2F4.  

So, you need solve this equation

    %28x-1%29%2F%28x%2B3%29 = 3%2F4.


To solve, cross-multiply

    4*(x-1) = 3*(x+3).


Simplify

    4x - 4 = 3x + 9

    4x - 3x = 9 + 4

       x    = 13.


Thus the original fraction is  %2813-4%29%2F13 = 9%2F13.    ANSWER


CHECK.  After adding 3 to both the numerator and denominator, you get  12%2F16 = 3%2F4.   ! correct !

Solved and explained.

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Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!
The solution from the other tutor is a good formal algebraic solution.

This particular type of problem can be solved more easily using an informal method.

The numerator of the original fraction is 4 less than the denominator; when 3 is added to both numerator and denominator, the numerator is still 4 less than the denominator.

The resulting fraction is equivalent to 3/4. In that fraction, the numerator is 1 less than the denominator. To get a fraction equivalent to 3/4 in which the numerator is 4 less than the denominator -- as required by the problem -- multiply numerator and denominator of the fraction 3/4 by 4 to get 12/16.

Then the fraction after adding 3 to both numerator and denominator is 12/16, which means the original fraction was 9/13.

ANSWER: 9/13