document.write( "Question 1013927: at a fast food restaurant, a family bought 4 hamburgers and 3 bags of french fries for 4.20. at the same time, a family traveling with them bought 5 hamburgers and 2 bags of french fries for 4.55. what was the cost of one hamburger and one bag of french fries? what was the cost if you ordered 5 hamburgers and 4 french fries?'
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #630251 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "At a fast food restaurant, a family bought 4 hamburgers and 3 bags of french fries for 4.20.
\n" ); document.write( "At the same time, a family traveling with them bought 5 hamburgers and 2 bags of french fries for 4.55.
\n" ); document.write( "What was the cost of one hamburger and one bag of french fries? What was the cost if you ordered 5 hamburgers and 4 french fries?'
\n" ); document.write( "------------------------------------------------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "From the condition, you have this system of two equations in two unknowns\r\n" );
document.write( "\r\n" );
document.write( "4h + 3f = 420,     (1)\r\n" );
document.write( "5h + 2f = 455.     (2)\r\n" );
document.write( "\r\n" );
document.write( "Here h is the price of one hamburger and f is the price of one bag of french fries in cents.\r\n" );
document.write( "\r\n" );
document.write( "To solve it, multiply equation (1) by 2 (both sides) and equation (2) by 3. You will get \r\n" );
document.write( "\r\n" );
document.write( " 8g + 6f =  840,   (1')\r\n" );
document.write( "15h + 6f = 1365.   (2')\r\n" );
document.write( "\r\n" );
document.write( "Now distract the equation (1') from (2') (both sides). In this way you eliminate the unknown f and obtain a single equation for unknown h:\r\n" );
document.write( "\r\n" );
document.write( "15h - 8h = 1365 - 840,   or\r\n" );
document.write( "\r\n" );
document.write( "7h = 525.\r\n" );
document.write( "\r\n" );
document.write( "Hence, h =  = 75.\r\n" );
document.write( "\r\n" );
document.write( "Substitute the found value of h = 75 into equation (1). You get\r\n" );
document.write( "\r\n" );
document.write( "3f = 420 - 4h = 420 -4*75 = 420 - 300 = 120,\r\n" );
document.write( "\r\n" );
document.write( "f =  = 40.\r\n" );
document.write( "\r\n" );
document.write( "Thus the cost of one hamburger is $0.75; the cost of one bag of french fries is $0.40.\r\n" );
document.write( "\r\n" );
document.write( "Now calculate the cost of 5 hamburgers and 4 french fries. It is\r\n" );
document.write( "\r\n" );
document.write( "5*$0.75 + 4*$0.40 = $5.35.\r\n" );
document.write( "

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

\n" );