document.write( "Question 392924: The sum of the digits of a three-digit number is 9. Four times the tens digit minus 3 times the units digit is 6. If 2 times the units digit is added to twice the hundreds digit, the result is 12. Find the number. Please help, thank you! \n" ); document.write( "
Algebra.Com's Answer #278937 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "You can do it woth or without algebra.  I'll do it both ways:\r\n" );
document.write( "\r\n" );
document.write( "------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Without algebra:\r\n" );
document.write( "\r\n" );
document.write( "If 2 times the units digit is added to twice the hundreds digit, \r\n" );
document.write( "the result is 12.\r\n" );
document.write( "\r\n" );
document.write( "That means that \r\n" );
document.write( "\r\n" );
document.write( "If 1 times the units digit is added to 1 times the hundreds digit,\r\n" );
document.write( "the result is 6.\r\n" );
document.write( "\r\n" );
document.write( "Since the sum of all three digits is 9, and the sum of the units and \r\n" );
document.write( "the hundreds digits is 6, the tens digit has to be 3.\r\n" );
document.write( "\r\n" );
document.write( "So, four times the tens digit is 12.\r\n" );
document.write( "\r\n" );
document.write( "We are told that four times the tens digit minus (3 times the units digit)\r\n" );
document.write( "is 6.\r\n" );
document.write( "\r\n" );
document.write( "So 12 minus (3 times the units digit) is 6.\r\n" );
document.write( "\r\n" );
document.write( "So (3 times the units digit) must be 6.\r\n" );
document.write( "\r\n" );
document.write( "Therefore the units digit is 2.\r\n" );
document.write( "\r\n" );
document.write( "And since the sum of all three digits is 9,  and the tens digit is 3\r\n" );
document.write( "and the units digit 2, the hundreds digit must be 4.\r\n" );
document.write( "\r\n" );
document.write( "So the number is 432.\r\n" );
document.write( " \r\n" );
document.write( "---------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "By algebra\r\n" );
document.write( "\r\n" );
document.write( "H + T + U = 9\r\n" );
document.write( "4T - 3U = 6\r\n" );
document.write( "2U + 2H = 12\r\n" );
document.write( "\r\n" );
document.write( "Solve that and get H=4, T=3 and U=2\r\n" );
document.write( "\r\n" );
document.write( "Edwin

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