document.write( "Question 999707: jack bought 34 stamps at the post office. some were 37cents and the rest were 80cents. if the total cost of the stamps was $16.45, how many of each type did he buy? \n" ); document.write( "

Algebra.Com's Answer #617253 by AnlytcPhil(1806) $\"\"$ $\"About$

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document.write( "Let the number of 37c stamps be x\r\n" );
document.write( "Let the number of 80c 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( "37c stamps    x       $0.37     $0.37x\r\n" );
document.write( "80c stamps    y       $0.80     $0.80y\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "TOTALS       34      -----     $16.45\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 = 34\r\n" );
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document.write( "  \r\n" );
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document.write( "           0.37x + 0.8y = 16.45\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( "          37x + 80y = 1645\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 = 34\r\n" );
document.write( "               y = 34 - x\r\n" );
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document.write( "Substitute (34 - x) for y in 37x + 80y = 1645\r\n" );
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document.write( "      37x + 80(34 - x) = 1645\r\n" );
document.write( "      37x + 2720 - 80x = 1645\r\n" );
document.write( "           -43x + 2720 = 1645\r\n" );
document.write( "                  -43x = -1075\r\n" );
document.write( "                x = 25 = the number of 37c stamps.\r\n" );
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document.write( "Substitute in y = 34 - x\r\n" );
document.write( "              y = 34 - (25\r\n" );
document.write( "              y = 9 80c stamps.\r\n" );
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document.write( "The number of 80c stamps is 34-y or 34-9 or 25 80c stamps.\r\n" );
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document.write( "Checking:  25 37c stamps is $9.25 and 9 80c stamps is $7.20\r\n" );
document.write( "            That's 34 stamps.\r\n" );
document.write( "            And indeed $9.25 + $7.20 = $16.45\r\n" );
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document.write( "Edwin

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