Question 1202448
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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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<pre>
Let x be the denominator.
Then the numerator is (x-4), according to the problem.


So, the original fraction is  {{{(x-4)/x}}}.


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

    {{{((x-4)+3)/(x+3)}}} = {{{(x-1)/(x+3)}}}.


It is equal to {{{3/4}}}.  

So, you need solve this equation

    {{{(x-1)/(x+3)}}} = {{{3/4}}}.


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  {{{(13-4)/13}}} = {{{9/13}}}.    <U>ANSWER</U>


<U>CHECK</U>.  After adding 3 to both the numerator and denominator, you get  {{{12/16}}} = {{{3/4}}}.   ! correct !
</pre>

Solved and explained.


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