document.write( "Question 196970: A food store makes a 9-lb mixture of peanuts, cashews, and raisins. Peanuts cost $1.50 per pound, cashews cost $2.00 per pound, and raisins cost $1.00 per pound. The mixture calls for twice as much peanuts than cashews. The total cost of the mixture is $13.00. How much of each ingredient did the store use? \n" ); document.write( "

Algebra.Com's Answer #147694 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
A food store makes a 9-lb mixture of peanuts, cashews, and raisins. Peanuts cost $1.50 per pound, cashews cost $2.00 per pound, and raisins cost $1.00 per pound. The mixture calls for twice as much peanuts than cashews. The total cost of the mixture is $13.00. How much of each ingredient did the store use?
\n" ); document.write( "

\r\n" );
document.write( "The sentence:\r\n" );
document.write( "\r\n" );
document.write( ">>...The mixture calls for twice as much \r\n" );
document.write( "                       peanuts than cashews...<<\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "tells us that we are defining peanuts IN TERMS OF cashews.\r\n" );
document.write( "We like to define things IN TERMS OF x\r\n" );
document.write( "\r\n" );
document.write( "So let x = the number of lbs. of cashews\r\n" );
document.write( "\r\n" );
document.write( "And then by that sentence,\r\n" );
document.write( "\r\n" );
document.write( "the number of lbs. of peanuts = twice x or 2x\r\n" );
document.write( "\r\n" );
document.write( "Let y = the number of lbs. of raisins. \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Make this chart:\r\n" );
document.write( "\r\n" );
document.write( "           No. of lbs. | Price per lb. | Price for all lbs.     \r\n" );
document.write( "Peanuts                |               |       \r\n" );
document.write( "Cashews                |               |                        \r\n" );
document.write( "Raisins                |               |           \r\n" );
document.write( "---------------------------------------------------------\r\n" );
document.write( "Mixture                |               |             \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Put in the expressions for the pounds of each ingredient, and\r\n" );
document.write( "the total number of pounds of Mixture: \r\n" );
document.write( "\r\n" );
document.write( "           No. of lbs. | Price per lb. | Price for all lbs.     \r\n" );
document.write( "Peanuts        2x      |               |               \r\n" );
document.write( "Cashews         x      |               |                        \r\n" );
document.write( "Raisins         y      |               |            \r\n" );
document.write( "---------------------------------------------------------\r\n" );
document.write( "Mixture         9      |               |           \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Put in the prices per lb. of each ingredient\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "           No. of lbs. | Price per lb. | Price for all lbs.     \r\n" );
document.write( "Peanuts        2x      |     1.50      |                 \r\n" );
document.write( "Cashews         x      |     2.00      |                        \r\n" );
document.write( "Raisins         y      |     1.00      |           \r\n" );
document.write( "---------------------------------------------------------\r\n" );
document.write( "Mixture         9      |               |           \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Multiply the no. of pounds by the price per pound to get the\r\n" );
document.write( "price for all the pounds.  Then put in 13.00 for the price\r\n" );
document.write( "for all the pounds of mixture: \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "           No. of lbs. | Price per lb. | Price for all lbs.     \r\n" );
document.write( "Peanuts        2x      |     1.50      |     2x(1.50)  \r\n" );
document.write( "Cashews         x      |     2.00      |      2.00x             \r\n" );
document.write( "Raisins         y      |     1.00      |      1.00y\r\n" );
document.write( "---------------------------------------------------------\r\n" );
document.write( "Mixture         9      |               |     13.00 \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Make the first equation from the \"no. of lbs.\" column:\r\n" );
document.write( "\r\n" );
document.write( "2x + x + y = 9\r\n" );
document.write( "\r\n" );
document.write( "Make the second equation form the \"Price for all lbs.\" column:\r\n" );
document.write( "\r\n" );
document.write( "2x(1.50) + 2.00x + 1.00y = 13.00\r\n" );
document.write( "\r\n" );
document.write( "------\r\n" );
document.write( "\r\n" );
document.write( "Simplify the first:\r\n" );
document.write( "\r\n" );
document.write( "2x + x + y = 9\r\n" );
document.write( "    3x + y = 9\r\n" );
document.write( "\r\n" );
document.write( "Simplify the second:\r\n" );
document.write( "\r\n" );
document.write( "2x(1.50) + 2.00x + 1.00y = 13.00\r\n" );
document.write( "            3x + 2x + 1y = 13\r\n" );
document.write( "                  5x + y = 13\r\n" );
document.write( "\r\n" );
document.write( "So we have this system:\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "Solve that and get x = 2, y = 3\r\n" );
document.write( "\r\n" );
document.write( "So there are x = 2 lbs. of cashews, \r\n" );
document.write( "2x = 2(2) = 4 lbs. of peanuts, and\r\n" );
document.write( "y = 3 lbs. of raisins.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );