document.write( "Question 1162698: A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. They used 100 black, 110 white and 90 red wires. How many of each cable were made? \n" ); document.write( "

Algebra.Com's Answer #786523 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "    3A + 1B + 2C = 100   (1)    (counting black cables)\r\n" );
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document.write( "    3A + 2B + 1C = 110   (2)    (counting white cables) \r\n" );
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document.write( "    2A + 1B + 2C =  90   (3)    (counting red cables)\r\n" );
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document.write( "To solve the system, subtract equation (3) from equation (1). You will get\r\n" );
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document.write( "     A            = 100 - 90 = 10.  \r\n" );
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document.write( "Substitute  this value  A= 10 into equations (1) and (2).  You will get then\r\n" );
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document.write( "    B + 2C  = 70    (4)\r\n" );
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document.write( "    2B + C  = 80    (5)\r\n" );
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document.write( "or equivalently\r\n" );
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document.write( "    2B + 4C = 140\r\n" );
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document.write( "    2B + C  =  80\r\n" );
document.write( "-------------------------- subtract\r\n" );
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document.write( "         3C = 140-80 = 60  ------>  C = 20.\r\n" );
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document.write( "Finally, from (4)  B = 70-2C = 70 - 40 = 30.\r\n" );
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document.write( "ANSWER.   A= 10;  B= 30;  C= 20.\r\n" );
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