document.write( "Question 1097639: A certain concrete mixture contains 5.00% cement and 7.00% sand ,How many kilograms of this mixture and how many kilograms of sand should be combined with 255 kg of cement to make a batch that is 16.0% cement and 18.0% sand? Carry out all calculations exactly and round to three significant digits final answers only.\r
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Algebra.Com's Answer #712137 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Let \"x\" be the amount/the mass of the original mixture which should be combined (in kilograms).\r\n" );
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document.write( "Let \"y\" be the amount/the mass of the (outside) sand which should be combined (in kilograms)\r\n" );
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document.write( "Then you have the system of these two equations for x and y:\r\n" );
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document.write( " = 0.16     (1)   (to provide the cement 16% content)\r\n" );
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document.write( "  = 0.18     (2)   (to provide the sand 18% contents)\r\n" );
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document.write( "Simplify by multiplying both sides of each equation by the respective denominator. You will get\r\n" );
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document.write( "0.05x + 255 = 0.16*(x + y + 255),     (3)\r\n" );
document.write( "0.07x  +  y = 0.18*(x + y + 255).     (4)\r\n" );
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document.write( "Simplify the system one step further by multiplying both sides of the equations by 100. You will get\r\n" );
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document.write( "5x + 25500  = 16*(x + y + 255),      (5)\r\n" );
document.write( "7x +   100y = 18*(x + y + 255).      (6)\r\n" );
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document.write( "Write the system in canonical/standard form\r\n" );
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document.write( "11x + 16y = 21420,                   (7)\r\n" );
document.write( "11x - 82y = -4590.                   (8)\r\n" );
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document.write( "The setup is completed. The rest is arithmetic and the technique for solving this system.\r\n" );
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document.write( "First step in solving is to subtract equation (8) from the equation (7). You will get\r\n" );
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document.write( "98y = 21420 + 4590 = 26010  ====>  y =  = 265.408 kg of of the (outside) sand.\r\n" );
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document.write( "Having the found value of y, you can calculate x from the equation (7)\r\n" );
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document.write( "x =  =  = 1561.225 kg.\r\n" );
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document.write( "Answer.  1561.225 kg of the original mixture and 265.408 kg of the (outside) sand should be added.\r\n" );
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document.write( "Check.  Eq(1):   = 0.16.\r\n" );
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document.write( "        Eq(2):   = 0.18.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Checked and proven to be correct solution.\r
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\n" ); document.write( "\n" ); document.write( " If you have another answer, I T I S W R O N G.\r
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