document.write( "Question 1132364: A 3 digit number such that it is equal to 19 times the sum of its digit. What is the largest possible value? example 114 = 19 * (1+1+4) or 133 = 19 * (1+3+3) \n" ); document.write( "

Algebra.Com's Answer #749382 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "ANSWER. The maximal such a number is 399.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Solution\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let \"a\" be the \"hundredth\" digit; \"b\" be the \"tens\" digit and \"c\" be the \"ones\" digit.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then the number is  100a + 10b + c,  and the condition says\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    100a + 10b + c = 19*(a+b+c),     or\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    81a  - 9b - 18c = 0,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     9a  - b - 2c = 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then  a= 3, b= 9  and c= 9   is \r\n" );
document.write( "\r\n" );
document.write( "    a) the solution to the last equation,    and \r\n" );
document.write( "\r\n" );
document.write( "    b) represents/provides the maximal such a number.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is obvious, taking into account that  0 <= a <= 9,  0 <= b<= 9,  0 <= c <= 9.\r\n" );
document.write( "

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

\n" );