document.write( "Question 697704: how much of a 25% acid solution should be mixed with 5 L of a 15% acid solution to obtain a 20% acid solution? \n" ); document.write( "
Algebra.Com's Answer #430232 by Edwin McCravy(20056) $\"\"$ $\"About$
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document.write( "The other tutor's answer is correct, but his method will work ONLY\r\n" );
document.write( "when the percentage desired is exactly half-way between the two\r\n" );
document.write( "percentages.  Here is a more general way to do the problem, which will\r\n" );
document.write( "work in ALL mixture problems: \r\n" );
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document.write( "Make this chart:\r\n" );
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document.write( "              amt of liquid     % acid   amt of pure acid contained \r\n" );
document.write( "1st solution       \r\n" );
document.write( "2nd solution        \r\n" );
document.write( "final solution\r\n" );
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document.write( "Let x be the answer, so fill that in first     \r\n" );
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document.write( "              amt of liquid     % acid   amt of pure acid contained \r\n" );
document.write( "1st solution        x           \r\n" );
document.write( "2nd solution      \r\n" );
document.write( "final solution     \r\n" );
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document.write( "We are told that there are 5 L of the second solution, so\r\n" );
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document.write( "              amt of liquid     % acid   amt of pure acid contained \r\n" );
document.write( "1st solution        x           \r\n" );
document.write( "2nd solution        5             \r\n" );
document.write( "final solution     \r\n" );
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document.write( "Now we add x PLUS 5 to get the amt of final liquid, so we fill\r\n" );
document.write( "x+5 in\r\n" );
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document.write( "              amt of liquid     % acid   amt of pure acid contained \r\n" );
document.write( "1st solution        x           \r\n" );
document.write( "2nd solution        5         \r\n" );
document.write( "final solution     x+5          \r\n" );
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document.write( "Next we fill in the three percentages as decimals:\r\n" );
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document.write( "              amt of liquid     % acid   amt of pure acid contained \r\n" );
document.write( "1st solution        x             .25           \r\n" );
document.write( "2nd solution        5             .15            \r\n" );
document.write( "final solution     x+5            .20          \r\n" );
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document.write( "Then we multiply the three amts of liquid by the percentages expressed\r\n" );
document.write( "as decimals to get the amt of pure acid in each amount:\r\n" );
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document.write( "              amt of liquid     % acid   amt of pure acid contained \r\n" );
document.write( "1st solution        x             .25            .23x\r\n" );
document.write( "2nd solution        5             .15            .15(5)\r\n" );
document.write( "final solution     x+5            .20            .20(x+5)\r\n" );
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document.write( "The equation comes from:\r\n" );
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document.write( "                 \r\n" );
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document.write( "                 .25x + .15(5) = .20(x+5)\r\n" );
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document.write( "Multiply through by 100  \r\n" );
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document.write( "                   25x + 15(5) = 20(x+5)\r\n" );
document.write( "                      25x + 75 = 20x + 100\r\n" );
document.write( "                            5x = 25\r\n" );
document.write( "                             x = 5              \r\n" );
document.write( "Edwin
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