document.write( "Question 173475: A food store makes a 9-lb mixture of peanuts. cashews, and raisens. Peanuts cost $1.50 per pound, cashews cost $2.00 per pound, and raisens 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?\r
\n" ); document.write( "\n" ); document.write( "How do you det this up into equations? \n" ); document.write( "
Algebra.Com's Answer #128338 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
These problems are always easier if you put letters in place
\n" ); document.write( "of the things you're looking for:
\n" ); document.write( "Let \"p\"= the pounds of peanuts needed
\n" ); document.write( "Let \"c\"= the pounds of cashews needed
\n" ); document.write( "Let \"r\"= the pounds of raisins needed
\n" ); document.write( "The 1st sentence says it's a 9-pound mixture, so
\n" ); document.write( "(1) \"p+%2B+c+%2B+r+=+9\"
\n" ); document.write( "Peanuts cost $1.50 per pound, so the cost of the peanuts will be
\n" ); document.write( "\"1.5p\"
\n" ); document.write( "Cashews cost $2.00 per pound, so the cost of the cashews will be
\n" ); document.write( "\"2c\"
\n" ); document.write( "Raisins cost $1.00 per pound, so the cost of the raisins will be
\n" ); document.write( "\"1%2Ar\"
\n" ); document.write( "The total cost of the mixture is $13.00, so
\n" ); document.write( "(2) \"1.5p+%2B+2c+%2B+r+=+13\"
\n" ); document.write( "The mixture calls for twice as much peanuts than cashews, so
\n" ); document.write( "(3) \"p+=+2c\"
\n" ); document.write( "Now I have 3 equations and 3 unknowns, so it should be solvable
\n" ); document.write( "Subtract (1) from (2)
\n" ); document.write( "\".5p+%2B+c+=+4\"
\n" ); document.write( "Substitute (3) for \"p\"
\n" ); document.write( "\".5%2A%282c%29+%2B+c+=+4\"
\n" ); document.write( "\"2c+=+4\"
\n" ); document.write( "\"c+=+2\"
\n" ); document.write( "And, going back to (3),
\n" ); document.write( "\"p+=+2c\"
\n" ); document.write( "\"p+=+2%2A2\"
\n" ); document.write( "\"p+=+4\"
\n" ); document.write( "Use (1) to find \"r\"
\n" ); document.write( "\"p+%2B+c+%2B+r+=+9\"
\n" ); document.write( "\"4+%2B+2+%2B+r+=+9\"
\n" ); document.write( "\"6+%2B+r+=+9\"
\n" ); document.write( "\"r+=+3\"
\n" ); document.write( "The amounts of the ingredients are 2 pounds of cashews,
\n" ); document.write( "4 pounds of peanuts, and 3 pounds of raisins
\n" ); document.write( "Check answer:
\n" ); document.write( "(2) \"1.5p+%2B+2c+%2B+r+=+13\"
\n" ); document.write( "\"1.5%2A4+%2B+2%2A2+%2B+3+=+13\"
\n" ); document.write( "\"6+%2B+4+%2B+3+=+13\"
\n" ); document.write( "\"13+=+13\"
\n" ); document.write( "OK \n" ); document.write( "
\n" );