document.write( "Question 220473: Help with word problem for Algebra 1\r
\n" ); document.write( "\n" ); document.write( "The nutty food company sells trail mixes by the pound. There are peanuts, raisin, ans carob-coated pretzels. The mgr. wants to make 80 pounds of this mixture and sell it for $3.35 per pound. Peanuts sell for $ $3.20 per pound, raisins sell for $ 2.40 per pound, and the carob pretzels sell for for $4.00 per pound. If the mixture has TWICE as many pounds of pretzels as raisons, how many pounds of each ingredient should the clerk use? \n" ); document.write( "

Algebra.Com's Answer #165527 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"p\"$ = pounds of peanuts needed
\n" ); document.write( "Let $\"r\"$ = pounds of raisins needed
\n" ); document.write( "Let $\"c\"$ = pounds of carob pretzels needed
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"p+%2B+r+%2B+c+=+80\"$
\n" ); document.write( "(2) $\"c+=+2r\"$
\n" ); document.write( "(2) $\"r+=+c%2F2\"$
\n" ); document.write( "Cost of peanuts in mixture = $\"3.2p\"$
\n" ); document.write( "Cost of raisins in mixture = $\"2.4r\"$
\n" ); document.write( "Cost of Carob pretzels in mixture = $\"4c\"$
\n" ); document.write( "--------------------------------------------
\n" ); document.write( "(3) $\"3.2p+%2B+2.4r+%2B+4c+=+3.35%2A80\"$
\n" ); document.write( "(3) $\"320p+%2B+240r+%2B+400c+=+26800\"$ (units are cents)
\n" ); document.write( "Multiply both sides of (1) by $\"240\"$ and
\n" ); document.write( "subtract from (3)
\n" ); document.write( "(3) $\"320p+%2B+240r+%2B+400c+=+26800\"$
\n" ); document.write( "(1) $\"-240p+-+240r+-+240c+=+-19200\"$
\n" ); document.write( " $\"80p+%2B+160c+=+7600\"$
\n" ); document.write( "Divide both sides by $\"80\"$
\n" ); document.write( " $\"p+%2B+2c+=+95\"$
\n" ); document.write( " $\"p+=+95+-+2c\"$
\n" ); document.write( "Substitute this result and (2) in (1)
\n" ); document.write( "(1) $\"p+%2B+r+%2B+c+=+80\"$
\n" ); document.write( " $\"95+-+2c+%2B+c%2F2+%2B+c+=+80\"$
\n" ); document.write( " $\"190+-+4c+%2B+c+%2B+2c+=+160\"$
\n" ); document.write( " $\"-c+=+-30\"$
\n" ); document.write( " $\"c+=+30\"$
\n" ); document.write( "and
\n" ); document.write( " $\"p+=+95+-+2c\"$
\n" ); document.write( " $\"p+=+95+-+2%2A30\"$
\n" ); document.write( " $\"p+=+95+-+60\"$
\n" ); document.write( " $\"p+=+35\"$
\n" ); document.write( "and
\n" ); document.write( " $\"r+=+c%2F2\"$
\n" ); document.write( " $\"r+=+30%2F2\"$
\n" ); document.write( " $\"r+=+15\"$
\n" ); document.write( "The clerk should use 35 lbs of peanuts, 15 lbs of raisins,
\n" ); document.write( "and 30 lbs of carob-coated pretzels
\n" ); document.write( "check answer:
\n" ); document.write( " $\"320p+%2B+240r+%2B+400c+=+26800\"$
\n" ); document.write( " $\"320%2A35+%2B+240%2A15+%2B+400%2A30+=+26800\"$
\n" ); document.write( " $\"11200+%2B+3600+%2B+12000+=+26800\"$
\n" ); document.write( " $\"26800+=+26800\"$
\n" ); document.write( "OK\r
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