document.write( "Question 1197547: How many kilograms of nickel silver containing 15% zinc and how many kilograms of nickel silver containing 33% zinc must be melted together to produce 748 kg of a new nickel silver containing 28% zinc? \n" ); document.write( "

Algebra.Com's Answer #830843 by ikleyn(52792) $\"\"$ $\"About$

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\n" ); document.write( "How many kilograms of nickel silver containing 15% zinc and how many kilograms
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document.write( "I take x kilograms of the 33% zink alloy\r\n" );
document.write( "and (748-x) kilograms of the 15% zink alloy.\r\n" );
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document.write( "For any x in between of 0 and 748 kg, the total mass of 748 kg alloy will be provided, correct ?\r\n" );
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document.write( "Hence, I only need to provide necessary concentration of 28% zink in the final mixture.\r\n" );
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document.write( "For it, I write an equation for the pure zink masses in components and in the final mixture\r\n" );
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document.write( "    0.15*(748-x) + 0.33x = 0.28*748 kilograms  for the mass of the pure zink.      (1)\r\n" );
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document.write( "The setup is done, and if you do understand it, you are great !\r\n" );
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document.write( "Now I will solve the equation to find x.\r\n" );
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document.write( "You should simplify it in couple of simple steps\r\n" );
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document.write( "    0.15*748 - 0.15x + 0.33x = 0.28*748\r\n" );
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document.write( "                    0.18x    = 0.28*748 - 0.15*748\r\n" );
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document.write( "                    0.18x    =      97.24\r\n" );
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document.write( "                        x    =      97.24/0.18 = 540.222 kilograms.\r\n" );
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document.write( "ANSWER.  540.222 kg of the 33% zinc alloy should be mixed with 748-540.222 = 207.778 kg of the 15% zinc alloy.\r\n" );
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document.write( "CHECK.  Mass of the pure zink in components, in total = 0.33*540.222 + 0.15*207.778 = 209.44 kg.\r\n" );
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document.write( "        Mass of the zink in the final mixture is  0.28*748 = 209.44 kg.\r\n" );
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document.write( "        We obtain the same mass in both sides of the equation (1), which means that the answer and the solution both are correct.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Now accept my congratulations, since from now you know how to solve mixture problems.\r
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