document.write( "Question 989797: A grocer mixes peanuts that cost $1.49 per pund and walnuts that cost $2.69 per pound to make 100 pounds of a mixture that costs $2.21 per pound. How much of each kind of nut did the grocer put into the mixture. \n" ); document.write( "

Algebra.Com's Answer #610032 by Edwin McCravy(20077) $\"\"$ $\"About$

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document.write( "Let the number of pounds of peanuts be x\r\n" );
document.write( "Let the number of pounds of walnuts be y\r\n" );
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document.write( "                      Value      Value\r\n" );
document.write( "Type       Number       of         of\r\n" );
document.write( " of          of          1        ALL\r\n" );
document.write( "nuts       pounds     pound     poundss\r\n" );
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document.write( "peanuts      x        $1.49     $1.49x\r\n" );
document.write( "walnuts      y        $2.69     $2.69y\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "mixture     100       $2.21   $221.00\r\n" );
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document.write( " The first equation comes from the second column.\r\n" );
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document.write( "  \r\n" );
document.write( "                 x + y = 100\r\n" );
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document.write( " The first equation comes from the last column.\r\n" );
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document.write( "  \r\n" );
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document.write( "           1.49x + 2.69y = 221\r\n" );
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document.write( "Get rid of decimals by multiplying every term by 100:\r\n" );
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document.write( "            149x + 269y = 22100\r\n" );
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document.write( " So we have the system of equations:\r\n" );
document.write( "           .\r\n" );
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document.write( "We solve by substitution.  Solve the first equation for y:\r\n" );
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document.write( "           x + y = 100\r\n" );
document.write( "               y = 100 - x\r\n" );
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document.write( "Substitute (100 - x) for y in 149x + 260y = 22100\r\n" );
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document.write( "    149x + 269(100 - x) = 22100\r\n" );
document.write( "    149x + 26900 - 269x = 22100\r\n" );
document.write( "          -120x + 26900 = 22100\r\n" );
document.write( "                  -120x = -4800\r\n" );
document.write( "                      x = 40 = the number of pounds of peanuts.\r\n" );
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document.write( "Substitute in y = 100 - x\r\n" );
document.write( "              y = 100 - (40)\r\n" );
document.write( "              y = 60 = the number of pounds of walnuts.\r\n" );
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document.write( "Checking:  40 peanuts is worth $59.60 and 60 pounds of walnuts is worth \r\n" );
document.write( "           $161.40\r\n" );
document.write( "           That's 100 pounds that is worth = $221\r\n" );
document.write( "           And 100 pounds of misture at 2.21 per pound is worth $221\r\n" );
document.write( "           So it checks.\r\n" );
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document.write( "Edwin

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