document.write( "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.
\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #837292 by ikleyn(52834)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "The numerator of a fraction is 4 less than its denominator,
\n" ); document.write( "if 3 is added both the numerator and denominator, the resulting number is 3/4.
\n" ); document.write( "what is the original fraction. Explain.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "Let x be the denominator.\r\n" );
document.write( "Then the numerator is (x-4), according to the problem.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the original fraction is  \"%28x-4%29%2Fx\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "After adding 3 to both the numerator and denominator, the fraction is  \r\n" );
document.write( "\r\n" );
document.write( "    \"%28%28x-4%29%2B3%29%2F%28x%2B3%29\" = \"%28x-1%29%2F%28x%2B3%29\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is equal to \"3%2F4\".  \r\n" );
document.write( "\r\n" );
document.write( "So, you need solve this equation\r\n" );
document.write( "\r\n" );
document.write( "    \"%28x-1%29%2F%28x%2B3%29\" = \"3%2F4\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To solve, cross-multiply\r\n" );
document.write( "\r\n" );
document.write( "    4*(x-1) = 3*(x+3).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify\r\n" );
document.write( "\r\n" );
document.write( "    4x - 4 = 3x + 9\r\n" );
document.write( "\r\n" );
document.write( "    4x - 3x = 9 + 4\r\n" );
document.write( "\r\n" );
document.write( "       x    = 13.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus the original fraction is  \"%2813-4%29%2F13\" = \"9%2F13\".    ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "CHECK.  After adding 3 to both the numerator and denominator, you get  \"12%2F16\" = \"3%2F4\".   ! correct !\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved and explained.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "----------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Do not forget to post your \"THANKS\" to me for my teaching.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );