document.write( "Question 522095: if x + 3y + 2z = 48 and 2x + 3y + 4z = 69, then the value of 3x + 3y + 6z is
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #346690 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
if x + 3y + 2z = 48 and 2x + 3y + 4z = 69, then the value of 3x + 3y + 6z is ?
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "The trick here is to observe that: \r\n" );
document.write( "\r\n" );
document.write( "1. the left side of the first equation contains x + 2z\r\n" );
document.write( "2. the left side of the second equation contains 2x + 4z, which is 2(x + 2z).\r\n" );
document.write( "3. the expression to find the value of contains 3x + 6z, which is 3(x + 2z)\r\n" );
document.write( "\r\n" );
document.write( "So we rewrite the problem by rearranging the terms\r\n" );
document.write( "

\n" ); document.write( "if x + 2z + 3y = 48 and 2x + 4z + 3y = 69, then the value of 3x + 6z + 3y is ?
\n" ); document.write( "

\r\n" );
document.write( "Then again by factoring the expressions 2x + 4z and 3x + 6z and writing x + 2z\r\n" );
document.write( "in parentheses:\r\n" );
document.write( "

\n" ); document.write( "if (x + 2z) + 3y = 48 and 2(x + 2z) + 3y = 69, then the value of 3(x + 2z) + y is ?
\n" ); document.write( "

\r\n" );
document.write( "Now let w = x + 2z and we can rewrite the problem again as\r\n" );
document.write( "

\n" ); document.write( "if w + 3y = 48 and 2w + 3y = 69, then the value of 3w + 3y is ?
\n" ); document.write( "

\r\n" );
document.write( "So we solve this system of equations:\r\n" );
document.write( "\r\n" );
document.write( " w + 3y = 48\r\n" );
document.write( "2w + 3y = 69\r\n" );
document.write( "\r\n" );
document.write( "and get w = 21, y = 9\r\n" );
document.write( "\r\n" );
document.write( "And therefore 3w + 3y = 3(w + y) = 3(21 + 9) = 3(30) = 90\r\n" );
document.write( "\r\n" );
document.write( "Answer = 90\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );