document.write( "Question 1200676: . Ulysses made two alcohol solutions of different concentrations. When he mixed 4 liters of the first solution with 6 liters if the second, he obtained 35% solution of alcohol. But when he mixed 6 liters of the first solution with 4 liters of the second, he obtained a 50% solution of alcohol. What would be the percentage of alcohol if he mixed 2 liters of first solution with 8 liters of the second?
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\n" ); document.write( " C. 25%
\n" ); document.write( " D. 72.5% \n" ); document.write( "

Algebra.Com's Answer #834875 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "Ulysses made two alcohol solutions of different concentrations.
\n" ); document.write( "When he mixed 4 liters of the first solution with 6 liters if the second,
\n" ); document.write( "he obtained 35% solution of alcohol.
\n" ); document.write( "But when he mixed 6 liters of the first solution with 4 liters of the second,
\n" ); document.write( "he obtained a 50% solution of alcohol.
\n" ); document.write( "What would be the percentage of alcohol if he mixed 2 liters of first solution
\n" ); document.write( "with 8 liters of the second?
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document.write( "Let x be the concentration of the alcohol in the first solution,\r\n" );
document.write( "      expressed as a decimal number.\r\n" );
document.write( "Let x be the concentration of the alcohol in the second solution.\r\n" );
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document.write( "Write equations for the concentrations as you read the problem\r\n" );
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document.write( "    4x + 6y = 0.35(4+6),  or  4x + 6y = 3.5,   (1)\r\n" );
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document.write( "    6x + 4y = 0.5*(6+4),  or  6x + 4y = 5.     (2)\r\n" );
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document.write( "To solve equations (1), (2), multiply eq(1) by 3; multiply eq(2) by 2.  You will get\r\n" );
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document.write( "    12x + 18y = 10.5    (1')\r\n" );
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document.write( "    12x +  8y = 10      (2')\r\n" );
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document.write( "Subtract eq(2') from eq(1')\r\n" );
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document.write( "          10y = 0.5  --->  y = 0.05.\r\n" );
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document.write( "Then from equation (2)\r\n" );
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document.write( "     6x = 5 - 4*0.05 = 4.8  --->  x = 4.8/6 = 0.8.\r\n" );
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document.write( "Thus the concentrations of the original mixtures are  x= 0.8,  y= 0.05.\r\n" );
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document.write( "Then the concentration of the desired mixture is  \r\n" );
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document.write( "    C =  =  =  = 0.2 = 20%.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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