document.write( "Question 887638: a 3-digit number is 99 more than itself reversed. the units digit exceeds the tens digit by 2 while the hundreds digit exceeds the unit digit by 1. what is the possible value of the original number? \n" ); document.write( "

Algebra.Com's Answer #536812 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
a 3-digit number is 99 more than itself reversed.
\n" ); document.write( "

\r\n" );
document.write( "      100h+10t+u = 100u+10t+h+99\r\n" );
document.write( "\r\n" );
document.write( "Simplify\r\n" );
document.write( "\r\n" );
document.write( "        99h-99u = 99\r\n" );
document.write( "\r\n" );
document.write( "Divide through by 99\r\n" );
document.write( "\r\n" );
document.write( "            h-u = 1\r\n" );
document.write( "

\n" ); document.write( "the units digit exceeds the tens digit by 2
\n" ); document.write( "

\r\n" );
document.write( "u=t+2\r\n" );
document.write( "

\n" ); document.write( "the hundreds digit exceeds the unit digit by 1
\n" ); document.write( "

\r\n" );
document.write( "h=u+1\r\n" );
document.write( "\r\n" );
document.write( "So we have to solve this system:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "h  -u=1\r\n" );
document.write( " -t+u=2  \r\n" );
document.write( "h  -u=1\r\n" );
document.write( "\r\n" );
document.write( "The augmented matrix is \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Its row reduced echelon form is \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Which becomes the system\r\n" );
document.write( "\r\n" );
document.write( "h  -u= 1 \r\n" );
document.write( "  t-u=-2\r\n" );
document.write( "\r\n" );
document.write( "h = u+1\r\n" );
document.write( "t = u-2\r\n" );
document.write( "\r\n" );
document.write( "So we can choose u as 2 through 8,\r\n" );
document.write( "Seven solutions:\r\n" );
document.write( "\r\n" );
document.write( "u=_, h=u+1=_, t=u-2=_, number=htu                              htu\r\n" );
document.write( "----------------------------------\r\n" );
document.write( "u=2, h=2+1=3, t=2-2=0, number=302\r\n" );
document.write( "u=3, h=3+1=4, t=3-2=1, number=413\r\n" );
document.write( "u=4, h=4+1=5, t=4-2=2, number=524\r\n" );
document.write( "u=5, h=5+1=6, t=5-2=3, number=635\r\n" );
document.write( "u=6, h=6+1=7, t=6-2=4, number=746\r\n" );
document.write( "u=7, h=7+1=8, t=7-2=5, number=857\r\n" );
document.write( "u=8, h=8+1=9, t=8-2=6, number=968\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );