document.write( "Question 1032006: A stationery company sells two types of notepads to college bookstores, the first wholesaling for 40¢ and the second for 70¢. The company receives an order for 570 notepads, together with a check for $282. If the order fails to specify the number of each type, how should the company fill the order? \n" ); document.write( "

Algebra.Com's Answer #647261 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "Let the number of cheaper notepads be x\r\n" );
document.write( "Let the number of costlier notepads be y\r\n" );
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document.write( "                       Cost       COST\r\n" );
document.write( "Type       Number       of         of\r\n" );
document.write( " of          of        EACH       ALL\r\n" );
document.write( "notepad   notepads   notepad    notepads\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "cheaper      x        $0.40      $0.40x\r\n" );
document.write( "costlier     y        $0.70      $0.70y\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "TOTALS     570        -----    $282.00\r\n" );
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document.write( " The first equation comes from the number of notepads column.\r\n" );
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document.write( "  \r\n" );
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document.write( "                 x + y = 570\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( "           0.40x + 0.70y = 282\r\n" );
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document.write( "Get rid of decimals by multiplying every term by 10:\r\n" );
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document.write( "                 4x + 7y = 2820\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 = 570\r\n" );
document.write( "               y = 570 - x\r\n" );
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document.write( "Substitute (570 - x) for y in 4x + 7y = 2820\r\n" );
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document.write( "   4x + 7(570 - x) = 2820\r\n" );
document.write( "    4x + 3990 - 7x = 2820\r\n" );
document.write( "        -3x + 3990 = 2820\r\n" );
document.write( "               -3x = -1170\r\n" );
document.write( "                 x = 390 = the number of cheaper notepads\r\n" );
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document.write( "Substitute in y = 570 - x\r\n" );
document.write( "              y = 570 - (390)\r\n" );
document.write( "              y = 180 costlier notepads\r\n" );
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document.write( "Checking:  390 cheaper notepads cost $156.00 and 180 costlier\r\n" );
document.write( "           notepads costs $126.00\r\n" );
document.write( "            That's 570 notepads.\r\n" );
document.write( "            And indeed $156.00 + $126.00 = $282.00\r\n" );
document.write( "Edwin

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