document.write( "Question 557615: A fraction has a value of 4/7. The two digits in the numerator are interchanged in the denominator. If 11 is added to the numerator, and 22 is subtracted from the denominator, the resulting fraction is the recipricol of the original fraction. Find the original fraction.\r
\n" ); document.write( "\n" ); document.write( "Thanks!(: \n" ); document.write( "

Algebra.Com's Answer #362679 by Edwin McCravy(20059) $\"\"$ $\"About$

You can put this solution on YOUR website!
A fraction has a value of 4/7. The two digits in the numerator are interchanged in the denominator. If 11 is added to the numerator, and 22 is subtracted from the denominator, the resulting fraction is the recipricol of the original fraction. Find the original fraction.
\n" ); document.write( "

\r\n" );
document.write( "tens digit of the numerator = t\r\n" );
document.write( "units digit of the numerator = u\r\n" );
document.write( "Numerator = 10t + u\r\n" );
document.write( "\r\n" );
document.write( ">>...The two digits in the numerator are interchanged in the denominator...<<\r\n" );
document.write( "\r\n" );
document.write( "tens digit of the denominator = u\r\n" );
document.write( "units digit of the denominator = t\r\n" );
document.write( "denominator = 10u + t\r\n" );
document.write( "\r\n" );
document.write( ">>...A fraction has a value of ...<<\r\n" );
document.write( "\r\n" );
document.write( " = \r\n" );
document.write( "\r\n" );
document.write( ">>...If 11 is added to the numerator, and 22 is subtracted from the\r\n" );
document.write( "denominator, the resulting fraction is the recipricol of the \r\n" );
document.write( "original fraction...<<\r\n" );
document.write( "\r\n" );
document.write( " = \r\n" );
document.write( "\r\n" );
document.write( "So we have this system of equations to solve:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We simplify the first equation:\r\n" );
document.write( "\r\n" );
document.write( " = \r\n" );
document.write( "\r\n" );
document.write( "Cross-multiply:\r\n" );
document.write( "\r\n" );
document.write( "7(10t + u) = 4(10u + t)\r\n" );
document.write( "\r\n" );
document.write( "  70t + 7u = 40u + 4t\r\n" );
document.write( "\r\n" );
document.write( "       66t = 33u \r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by 33\r\n" );
document.write( "\r\n" );
document.write( "        2t = u \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Cross-multiply:\r\n" );
document.write( "\r\n" );
document.write( "4(10t + u + 11) = 7(10u + t - 22)\r\n" );
document.write( "  40t + 4u + 44 = 70u + 7t - 154\r\n" );
document.write( "      33t + 198 = 66u \r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by 33\r\n" );
document.write( "\r\n" );
document.write( "          t + 6 = 2u \r\n" );
document.write( "\r\n" );
document.write( "So the system is now\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Solve that by substitution and get\r\n" );
document.write( "\r\n" );
document.write( "t = 2, u = 4 \r\n" );
document.write( "\r\n" );
document.write( "numerator = 10t + u = 10(2) + 4 = 20 + 4 = 24\r\n" );
document.write( "denominator = 10u + t = 10(4) + 2 = 40 + 2 = 42\r\n" );
document.write( "\r\n" );
document.write( "fraction = \r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );