document.write( "Question 990992: how many liters of 20 percent alcohol solution and how many liters of pure alcohol should be mixed to obtain 8 liters of a 70% alcohol solution ? \n" ); document.write( "

Algebra.Com's Answer #610919 by Edwin McCravy(20056) $\"\"$ $\"About$

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how many liters of 20 percent alcohol solution and how many liters of pure alcohol should be mixed to obtain 8 liters of a 70% alcohol solution ?
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document.write( "We are mixing x liters of a weak alcohol solution with y liters of pure\r\n" );
document.write( "alcohol and we are ending up with 8 liters of liquid of medium strength.\r\n" );
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document.write( "So looking only at the number of liters of liquid we have:\r\n" );
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document.write( "equation (1)  x + y = 8\r\n" );
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document.write( "Now let's get the pure alcohol out of each of the three terms of equation (1)\r\n" );
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document.write( "First term x [on the left side of equation (1)]\r\n" );
document.write( "Out of the x liters of weaker solution, only 20% of it is pure, the rest water.\r\n" );
document.write( "So out of the first term, x,  in equation (1) we get 20%x or 0.20x or 0.2x liters of pure alcohol.   \r\n" );
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document.write( "Second term y [on the left side of equation (1)]\r\n" );
document.write( "Out of the y liters of pure alcohol, all 100% of it is pure, and no water.\r\n" );
document.write( "So out of the second term, y,  in equation (1) we get 100%y or 1y or y liters of pure alcohol.\r\n" );
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document.write( "Third term [on the right side of equation (1)]\r\n" );
document.write( "Out of the 8 liters of final mixture, only 70% of it is pure, the rest water.\r\n" );
document.write( "So out of the third term, 8,  in equation (1) we get 70%*8 or 0.70*8 or 5.6 \r\n" );
document.write( "liters of pur alcohol in the final mixture.\r\n" );
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document.write( "So the other equation is just equation (1) with each term multiplied by the\r\n" );
document.write( "percentage of pure alcohol it contaions.\r\n" );
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document.write( "So we have \r\n" );
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document.write( "equation(2)  0.2x + y = 5.6\r\n" );
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document.write( "So solve the system of equations (1) and (2):\r\n" );
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document.write( "The first equation is the \"liquid\" equation and the second equation is the\r\n" );
document.write( "\"pure alcohol\" equation.  The first equation is easy x+y=8.  Then the second \r\n" );
document.write( "equation is just the first equation with each term multiplied by the percent\r\n" );
document.write( "of alcohol in each term of the first equation.  \r\n" );
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document.write( "Solve that by substitution or elimination and get x=3 liters and y=5 liters.\r\n" );
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document.write( "That answer is reasonable because 70% is a lot stronger than 20%, so it'll\r\n" );
document.write( "take more of the pure stuff and less of the weaker to bring the 20% up to 70%,\r\n" );
document.write( "so it makes sense that we would 5 liters of pure and only 3 liters of the weak\r\n" );
document.write( "solution.\r\n" );
document.write( "Edwin

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