document.write( "Question 1025769: a lab tech needs to make a 60-liter batch of a 40% acid solution, how can the lab tech combine a batch of an acid solution that is pure acid with another that is 20% to get desired concentration \n" ); document.write( "
Algebra.Com's Answer #641086 by ikleyn(52797)\"\" \"About 
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\n" ); document.write( "a lab tech needs to make a 60-liter batch of a 40% acid solution, how can the lab tech combine a batch of an acid solution that is pure acid with another that is 20% to get desired concentration
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document.write( "Let x = the volume of the pure acid (in liters),\r\n" );
document.write( "and y = the volume of the 20% acid solution to combine with.\r\n" );
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document.write( "Then you have two equations \r\n" );
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document.write( "x +    y = 60,       (1)    (for the total combined volume)\r\n" );
document.write( "x + 0.2y = 0.4*60.   (2)    (for the acide amount)\r\n" );
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document.write( "Rewrite the system by simplifying (2):\r\n" );
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document.write( "x +    y = 60,       (1')\r\n" );
document.write( "x + 0.2y = 24.       (2')\r\n" );
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document.write( "From (1'), express x = 60-y and substitute it into (2'). You will get a single equation for the unknown y:\r\n" );
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document.write( "(60-y) + 0.2y = 24.\r\n" );
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document.write( "Simplify and solve it:\r\n" );
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document.write( "60 - y + 0.2y = 24,\r\n" );
document.write( "60 - 0.8y = 24,\r\n" );
document.write( "60 - 24 = 0.8y,\r\n" );
document.write( "36 = 0.8y,\r\n" );
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document.write( "y = \"36%2F0.8\" = 45 liters of the 40% acid solution.\r\n" );
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document.write( "Now, x = 60 - 45 = 15 liters of pure acid.\r\n" );
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