document.write( "Question 1178068: A chemist needs 8 liters of a 25% acid solution. The solution is to be mixed from three solutions whose concentrations are 10%, 20%, and 50%. How many liters of each solution will satisfy each condition?
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Algebra.Com's Answer #807237 by ikleyn(52797) $\"\"$ $\"About$

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\n" ); document.write( "A chemist needs 8 liters of a 25% acid solution. The solution is to be mixed from three solutions
\n" ); document.write( "whose concentrations are 10%, 20%, and 50%. How many liters of each solution will satisfy each condition?
\n" ); document.write( "a. Use as little as possible of the 50% solution
\n" ); document.write( "b. Use as much as possible of the 50% solution.
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document.write( "(a)  It is intuitively clear that if you want to use as little as possible of the 50% solution,\r\n" );
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document.write( "     you should not use 10% solution at all, and should use the 20% solution, mixing it with the 50% solution.\r\n" );
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document.write( "    In this case, let x liters be the amount of the 50% solution to use \r\n" );
document.write( "              and let (8-x) liters be the amount of the 20% to add.\r\n" );
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document.write( "    Then you have this equation for the pure acid volume\r\n" );
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document.write( "        0.5x + 0.2*(8-x) = 0.25*8\r\n" );
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document.write( "    From the equation,  x =  =  = 1 .\r\n" );
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document.write( "    ANSWER.  1  liters of the 50% acid solution and the rest, 6  liters of the 20% acid solution.\r\n" );
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document.write( "(b)  It is intuitively clear that if you want to use as much as possible of the 50% solution,\r\n" );
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document.write( "     you should not use 20% solution at all, and should use the 10% solution, mixing it with the 50% solution.\r\n" );
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document.write( "    In this case, let x liters be the amount of the 50% solution to use \r\n" );
document.write( "              and let (8-x) liters be the amount of the 10% to add.\r\n" );
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document.write( "    Then you have this equation for the pure acid volume\r\n" );
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document.write( "        0.5x + 0.1*(8-x) = 0.25*8\r\n" );
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document.write( "    From the equation,  x =  =  = 3.\r\n" );
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document.write( "    ANSWER.  3 liters of the 50% acid solution and the rest, 5 liters of the 10% acid solution.\r\n" );
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