document.write( "Question 979391: A vending machine sells chips at $0.55 and candy at $0.75. Last month, the vending machine yielded $189.00 with the sale of 280 items.
\n" ); document.write( "Let x be the number of chips sold and y the number of candies. How many packages of chips were purchased last month? \n" ); document.write( "

Algebra.Com's Answer #600659 by Edwin McCravy(20060) $\"\"$ $\"About$

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A vending machine sells chips at $0.55 and candy at $0.75. Last month, the
\n" ); document.write( "vending machine yielded $189.00 with the sale of 280 items.
\n" ); document.write( "Let x be the number of chips sold and y the number of candies. How many packages
\n" ); document.write( "of chips were purchased last month?\r
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document.write( "Let the number of chips be x\r\n" );
document.write( "Let the number of candies be y\r\n" );
document.write( "                      Value      Value\r\n" );
document.write( "Type       Number       of         of\r\n" );
document.write( " of          of        EACH       ALL\r\n" );
document.write( "item        items      item      items\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "chips         x      $0.55     $0.55x\r\n" );
document.write( "candies       y      $0.75     $0.75y\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "TOTALS      280      -----     $1890\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 = 280\r\n" );
document.write( "  \r\n" );
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document.write( "0.55x + 0.75y = 1890\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( "     55x + 75y = 18900\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 = 280\r\n" );
document.write( "      y = 280 - x\r\n" );
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document.write( "Substitute (280 - x) for y in 55x + 75y = 18900\r\n" );
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document.write( "     55x + 75(280 - x) = 18900\r\n" );
document.write( "     55x + 21000 - 75x = 18900\r\n" );
document.write( "          -20x + 21000 = 18900\r\n" );
document.write( "                  -20x = -2100\r\n" );
document.write( "                     x = 105 = the number of chips.\r\n" );
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document.write( "Substitute in y = 280 - x\r\n" );
document.write( "              y = 280 - (105)\r\n" );
document.write( "              y = 175 candies.\r\n" );
document.write( "The number of candies is 280-x or 280-105 or 175 candies.\r\n" );
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document.write( "Checking:  105 chips is $0.55*105 = $57.75 and \r\n" );
document.write( "           175 candies is $0.75*175 = $131.25\r\n" );
document.write( "            That's 280 items.\r\n" );
document.write( "            And indeed $57.75 + $131.25 = $189.00\r\n" );
document.write( "Edwin

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