document.write( "Question 462698: four-digit numbers between 3600 and 3699 where one digit equals the sum of the other three \n" ); document.write( "
Algebra.Com's Answer #317411 by Edwin McCravy(20063)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "The thousands digit is 3, and the hundredths digit is 6.\r\n" );
document.write( "Let the tens digit be a, and ones digit be b\r\n" );
document.write( "\r\n" );
document.write( "3+6+a=b or 3+6+b=a or 3+a+b=6 or 6+a+b=3\r\n" );
document.write( "\r\n" );
document.write( "That is,\r\n" );
document.write( "\r\n" );
document.write( "9+a=b, 9+b=a, a+b=3, or a+b=-3\r\n" );
document.write( "\r\n" );
document.write( "The last one is out, so we have\r\n" );
document.write( "\r\n" );
document.write( "9+a=b, 9+b=a, a+b=3\r\n" );
document.write( " \r\n" );
document.write( "The only solution for 9+a=b is a=0, b=9, which gives 3609\r\n" );
document.write( "\r\n" );
document.write( "The only solution for 9+b=a is b=0, a=9, which gives 3690\r\n" );
document.write( "\r\n" );
document.write( "The solution for a+b=3 are\r\n" );
document.write( "\r\n" );
document.write( " a=0, b=3, which gives 3603\r\n" );
document.write( " a=1, b=2, which gives 3612\r\n" );
document.write( " a=2, b=1, which gives 3621\r\n" );
document.write( " a=3, b=0, which gives 3630\r\n" );
document.write( "\r\n" );
document.write( "So all 6 solutions are:\r\n" );
document.write( "\r\n" );
document.write( "1.  3603\r\n" );
document.write( "2.  3609\r\n" );
document.write( "3.  3612\r\n" );
document.write( "4.  3621\r\n" );
document.write( "5.  3630\r\n" );
document.write( "6.  3690\r\n" );
document.write( "\r\n" );
document.write( "Edwin

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