document.write( "Question 816506: The sum of 128 and the square of its tens digit is 24 times its tens digit \n" ); document.write( "
Algebra.Com's Answer #491556 by Edwin McCravy(20086)\"\" \"About 
You can put this solution on YOUR website!
The sum of 128 and the square of its tens digit is 24 times its tens digit.
\n" ); document.write( "
\r\n" );
document.write( "Is that really what you meant?  With no mention of the units digit?\r\n" );
document.write( "\r\n" );
document.write( "      128+tē = 24t\r\n" );
document.write( "  tē-24t+128 = 0\r\n" );
document.write( " (t-8)(t-16) = 0\r\n" );
document.write( "\r\n" );
document.write( "t-8 = 0;  t-16 = 0\r\n" );
document.write( "  t = 8;     t = 16\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So the tens digit is 8.  it could be any number with the tens digit 8.\r\n" );
document.write( "\r\n" );
document.write( "It could be 80, 87, 286, 6784, or any number that has 8 for its next to\r\n" );
document.write( "the last digit.  Are you sure you copied the problem right?\r\n" );
document.write( "\r\n" );
document.write( "-------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Maybe you meant this:\r\n" );
document.write( "\r\n" );
document.write( "The sum of 128 and the square of its tens digit is 24 times its UNITS digit.\r\n" );
document.write( "\r\n" );
document.write( "Then 128+tē = 24u\r\n" );
document.write( "         tē = 24u-128\r\n" );
document.write( "          \r\n" );
document.write( "The smallest t could be is 0 and the largest it could be is 9\r\n" );
document.write( "So:\r\n" );
document.write( "         0 ≦ t ≦ 9\r\n" );
document.write( "so\r\n" );
document.write( "        0 ≦ tē ≦ 81\r\n" );
document.write( "\r\n" );
document.write( "       0 ≦ 24u-128 ≦ 81\r\n" );
document.write( "\r\n" );
document.write( "     128 ≦ 24u ≦ 209\r\n" );
document.write( "\r\n" );
document.write( "      5.3 < u < 8.7\r\n" );
document.write( "\r\n" );
document.write( "So u can only be 6, 7 or 8   \r\n" );
document.write( "\r\n" );
document.write( "If u = 6, then tē = 24u-128 = 24(6)-128=144-128 = 16, and t=4.\r\n" );
document.write( "So one solution is 46.\r\n" );
document.write( "\r\n" );
document.write( "If u = 7, then tē = 24u-128 = 24(7)-128=168-128 = 40, which has \r\n" );
document.write( "no integer square root.  So we discard u=7.\r\n" );
document.write( "\r\n" );
document.write( "If u = 8, then tē = 24u-128 = 24(8)-128=192-128 = 64, and t=8.\r\n" );
document.write( "So the only other solution is 88.\r\n" );
document.write( "\r\n" );
document.write( "If the above was what you mean, the two solutions are 46 and 88.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );