document.write( "Question 478004: The sum of two numbers is 248. Their difference is 64. find the number. \n" ); document.write( "

Algebra.Com's Answer #852392 by ikleyn(52879) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "The sum of two numbers is 248. Their difference is 64. find the number.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        The solution to this problem in the post by @Theo, giving the answer   x = 164, y = 100,   is incorrect. \r
\n" ); document.write( "\n" ); document.write( "        It does not satisfy the condition   x+y = 248.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        I came to bring a correct solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let x be the greater number, y be the smaller number.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We have then these two equations\r\n" );
document.write( "\r\n" );
document.write( "    x + y = 248,    (1)\r\n" );
document.write( "\r\n" );
document.write( "    x - y =  64.    (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You can solve this system of two linear equations by the Substitution method\r\n" );
document.write( "or by the Elimination method, on your choice.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Let' solve by the Elimination method.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Add equations (1) and (2).  The terms with 'y' will annihilate,\r\n" );
document.write( "and you will get\r\n" );
document.write( "\r\n" );
document.write( "    2x = 248 + 64 = 312,\r\n" );
document.write( "\r\n" );
document.write( "     x            = 312/2 = 156.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now find 'y' from equation (1)\r\n" );
document.write( "\r\n" );
document.write( "    y = 248 - x = 248 - 156 = 184.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  x = 156, y = 92.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "CHECK.  x + y = 156 + 92 = 248  (correct).  x - y = 156 - 92 = 64  (correct).\r\n" );
document.write( "

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

\n" );