document.write( "Question 1145714: On the first day of a two day meeting, 10 coffees and 10 doughnuts were purchased for a total of $20.00. Since nobody drank the coffee and all the doughnuts were eaten, the next day only 2 coffees and 14 doughnuts were purchased for a total of $13.00. How much did each coffee and each doughnut cost? \n" ); document.write( "

Algebra.Com's Answer #766996 by ikleyn(52814) $\"\"$ $\"About$

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

\r\n" );
document.write( "\r\n" );
document.write( "First appearance of the system\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    10x + 10y = 20    (1)\r\n" );
document.write( "\r\n" );
document.write( "     2x + 14y = 13    (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Multiply equation (2) by 5 (both sides).  Keep equation (1) as is.\r\n" );
document.write( "\r\n" );
document.write( "Second appearance of the system\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    10x + 10y = 20    (1')\r\n" );
document.write( "\r\n" );
document.write( "    10x + 70y = 65    (2')\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now subtract equation (1') from equation (2').  The terms \"10x\" will cancel each other (ELIMINATION !), and you will get\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "          60y = 45,\r\n" );
document.write( "\r\n" );
document.write( "            y =  =  of the dollar = $0.75.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next substitute y = 0.75 into equation (1') to get\r\n" );
document.write( "\r\n" );
document.write( "     10x = 20 - 10*0.75 = 12.50,\r\n" );
document.write( "\r\n" );
document.write( "       x = 1.25.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The price for each coffee is $1.25;  for each doughnut $0.75.\r\n" );
document.write( "

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

\n" );