document.write( "Question 1007859: ann purchased 40 stamps, a mixture of 44 cent stamps and 20 cent stamps. Find the number of each type of stamp if she spent $13.28. Using a system of equations to solve. \n" ); document.write( "

Algebra.Com's Answer #623709 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "Let the number of 44¢ stamps be x\r\n" );
document.write( "Let the number of 20¢ stamps 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        EACH       ALL\r\n" );
document.write( "stamp      stamps     stamp     stamps\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "44¢s         x        $0.44     $0.44x\r\n" );
document.write( "20¢s         y        $0.20     $0.20y\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "TOTALS      40       -----     $13.28\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" );
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document.write( "                 x + y = 40\r\n" );
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document.write( " The second equation comes from the last column.\r\n" );
document.write( "  \r\n" );
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document.write( "           0.44x + 0.20y = 13.28\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( "          44x + 20y = 1328\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 = 40\r\n" );
document.write( "               y = 40 - x\r\n" );
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document.write( "Substitute (40 - x) for y in 44x + 20y = 1328\r\n" );
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document.write( "   44x + 20(40 - x) = 1328\r\n" );
document.write( "    44x + 800 - 20x = 1328\r\n" );
document.write( "          24x + 800 = 1328\r\n" );
document.write( "                24x = 528\r\n" );
document.write( "                  x = 22 = the number of 44¢s.\r\n" );
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document.write( "Substitute in y = 40 - x\r\n" );
document.write( "              y = 40 - (22)\r\n" );
document.write( "              y = 18 = the number of 20¢s.\r\n" );
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document.write( "Checking:  22 44¢s is $9.68 and 18 20¢s is $3.60\r\n" );
document.write( "            That's 40 stamps.\r\n" );
document.write( "            And indeed $9.68 + $3.60 = $13.28\r\n" );
document.write( "Edwin

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