document.write( "Question 1027852: mixing a given quantity of 30% silver alloy with a quantity of 90% silver yields 200 units of a 54% silver alloy. How many units of each alloy were used \n" ); document.write( "

Algebra.Com's Answer #643050 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "mixing a given quantity of 30% silver alloy with a quantity of 90% silver yields 200 units of a 54% silver alloy.
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document.write( "Let x = a mass of the 30% silver alloy used, and \r\n" );
document.write( "    y = a mass of the 90% silver alloy used.\r\n" );
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document.write( "Then the total mass equation is \r\n" );
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document.write( "x + y = 200,\r\n" );
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document.write( "and the \"pure silver\" mass equation is\r\n" );
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document.write( "0.3x + 0.9y = 0.54*200.\r\n" );
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document.write( "Simplify these equations and collect them into a system of equations\r\n" );
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document.write( "x + y  = 200,        (1)\r\n" );
document.write( "0.3x + 0.9y = 108.   (2)\r\n" );
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document.write( "To solve it, express  x = 200 - y from  (1)  and substitute it into  (2). You will get a single equation for y:\r\n" );
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document.write( "0.3*(200 - y) + 0.9y = 108,\r\n" );
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document.write( "60 - 0.3y + 0.9y = 108,\r\n" );
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document.write( "0.6y = 108 - 60   --->   0.6y = 48   --->   y =  = 80.\r\n" );
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document.write( "Thus the mass of the 90% silver alloy used was 80 units.\r\n" );
document.write( "The mass of the 30% silver alloy used was 200-80 = 120 units.\r\n" );
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