document.write( "Question 1033124: A certain quantity was taken from a ten liter 30% alcohol solution and replaced by pure alcohol so as to produce 51% alcohol solution. How many liters were taken and replaced? \n" ); document.write( "

Algebra.Com's Answer #647729 by Edwin McCravy(20056) $\"\"$ $\"About$

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A certain quantity was taken from a ten liter 30% alcohol
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document.write( "Let the number of liters of pure added be x\r\n" );
document.write( "Let the number of liters of 30%alcohol left\r\n" );
document.write( "    in the jug after the x liters were \r\n" );
document.write( "    taken out and replaced be \r\n" );
document.write( "    y liters of pure alcohol\r\n" );
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document.write( "                         Percent      Liters\r\n" );
document.write( "                         alcohol     of pure\r\n" );
document.write( "  Type        Liters       in        alcohol\r\n" );
document.write( "   of          of         EACH      contained\r\n" );
document.write( "liquid       liquid    as decimal    in each\r\n" );
document.write( "---------------------------------------------\r\n" );
document.write( "pure alcohol    x         1.00       1.00x\r\n" );
document.write( "30% alcohol     y         0.30       0.30y\r\n" );
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document.write( "Final mixture  10         0.51      (0.51)(10) = 5.1\r\n" );
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document.write( " The first equation comes from the second column.\r\n" );
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document.write( "  \r\n" );
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document.write( "                 x + y = 10\r\n" );
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document.write( " The second equation comes from the last column.\r\n" );
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document.write( "           1.00x + 0.30y = 5.1\r\n" );
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document.write( "Get rid of decimals by multiplying every term by 10:\r\n" );
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document.write( "          10x + 3y = 51\r\n" );
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document.write( " So we have the system of equations:\r\n" );
document.write( "           .\r\n" );
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document.write( "We solve by substitution.  Solve the first equation for y:\r\n" );
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document.write( "           x + y = 10\r\n" );
document.write( "               y = 10 - x\r\n" );
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document.write( "Substitute (10 - x) for y in 10x + 3y = 51\r\n" );
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document.write( "     10x + 3(10 - x) = 51\r\n" );
document.write( "       10x + 30 - 3x = 51\r\n" );
document.write( "             7x + 30 = 51\r\n" );
document.write( "                  7x = 21\r\n" );
document.write( "answer:            x = 3 liters drained and \r\n" );
document.write( "                         replaced with pure alcohol\r\n" );
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document.write( "Edwin

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