document.write( "Question 1007274: a metal worker has a 30% copper and another alloy that is 60% copper. how many killograms of each alloy should the metal worker combine to create 80 kg of a 48% copper alloy \n" ); document.write( "

Algebra.Com's Answer #623255 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "Let the number of kgs. of Alloy1 be x\r\n" );
document.write( "Let the number of kgs. of Alloy2 be y\r\n" );
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document.write( "                                 Number\r\n" );
document.write( "Type       Number   Percent      of kg\r\n" );
document.write( " of        of kg    which is    of copper\r\n" );
document.write( "coin      of metal   copper     in each\r\n" );
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document.write( "Alloy1       x       0.30        0.30x\r\n" );
document.write( "Alloy2       y       0.60        0.60y\r\n" );
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document.write( "mixture     80      0.48        0.48(80)\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 = 80\r\n" );
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document.write( " The second equation comes from the last column.\r\n" );
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document.write( "           0.3x + 0.6y = 0.48(80)\r\n" );
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document.write( "           0.3x + 0.6y = 38.4\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( "               3x + 6y = 384\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 = 80\r\n" );
document.write( "               y = 80 - x\r\n" );
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document.write( "Substitute (80 - x) for y in 30x + 60y = 3840\r\n" );
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document.write( "      3x + 6(80 - x) = 384\r\n" );
document.write( "       3x + 480 - 6x = 384\r\n" );
document.write( "           -3x + 480 = 384\r\n" );
document.write( "                 -3x = -96\r\n" );
document.write( "                   x = 32 = the number of kg. of Alloy1.\r\n" );
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document.write( " Substitute in y = 80 - x\r\n" );
document.write( "               y = 80 - 32 = 48 kg. of Alloy2. \r\n" );
document.write( "Edwin

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