document.write( "Question 1129615: Use a system of linear equations with two variables and two equations to solve. \r
\n" ); document.write( "\n" ); document.write( "A moving company charges a flat rate of $120, and an additional $8 for each box. If a taxi service would charge $20 for each box, what is the minimum number of boxes you would need for it to be cheaper to use the moving company? \r
\n" ); document.write( "\n" ); document.write( "What would be the total cost? \n" ); document.write( "

Algebra.Com's Answer #746182 by ikleyn(52798) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "The system is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "y = 120 + 8x,    (1)\r\n" );
document.write( "y = 20x,         (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "where x is the number of boxes and y is the total cost.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To solve the system, notice that the left sides of the two equations are identical - so their right sides should be equal:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "120 + 8x = 20x     (getting this equation is identical to substitution eq(1) into eq(2)).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "120 = 20x - 8x\r\n" );
document.write( "\r\n" );
document.write( "12x = 120  ====>  x = 120/12 = 10.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  10 boxes is break even.  Moving company is cheaper if the number of boxes is 11 or greater.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then the total cost by the moving company would be 120+11*8 = 208 dollars,\r\n" );
document.write( "\r\n" );
document.write( "                                  while by taxi it would be 11*20 = 220 dollars.\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Notice : Usually (as a rule) such problems students solve using one single equation or inequality.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );