Question 1201447
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The denominator of a fraction is 8 more than the numerator. If both the numerator and denominator 
are decreased by 5, then the resulting fraction becomes 2/3. Find the original fraction
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It can be easily solved using one unknown and one equation.



<pre>
Let x be the numerator of the fraction.

Then the denominator is (x+8).


Decreased values are (x-5) for the numerator and ((x+8)-5) = (x+3) for the denominator.


Write equation for modified fraction

    {{{(x-5)/(x+3)}}} = {{{2/3}}}.


Cross-multiply and find x

    3(x-5) = 2(x+3),

    3x - 15 = 2x + 6,

    3x - 2x = 6 + 15.

       x    =   21.


The original fraction is  {{{21/(21+8)}}} = {{{21/29}}}.    <<<---===  <U>ANSWER</U>
</pre>

Solved.