document.write( "Question 1195880: Alligation method
\n" ); document.write( "You need a 200mL stock solution of 10mg/mL aminophylline to prepare several unit-dose oral syringes. You carry the standard 25mg/mL aminophylline solution. How much water and standard aminophylline (25mg/mL) do you combine to create this new solution?
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Algebra.Com's Answer #828490 by greenestamps(13206) $\"\"$ $\"About$

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\n" ); document.write( "The response from the other tutor shows a standard algebraic method for solving the problem.

\n" ); document.write( "If you actually want to solve the problem using the alligation method, then it might look something like this:

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document.write( "     25    10 (=10-0)\r\n" );
document.write( "       \  /\r\n" );
document.write( "        10\r\n" );
document.write( "       /  \\r\n" );
document.write( "     0     15 (=25-10)\r\n" );
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document.write( "The 25 and 0 at the left are the concentrations in mg/mL of the two ingredients.\r\n" );
document.write( "The 10 in the middle is the desired concentration.\r\n" );
document.write( "The 10 and 15 at the right represent the ratio in which the two ingredients must be mixed -- 10:15, or 2:3.  (Those numbers are the differences, calculated diagonally, between the numbers on the left and the number in the middle.)\r\n" );
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document.write( "The ratio 2:3 means 2/5 of the mixture should be the first ingredient and 3/5 should be the second.  So 2/5 of the 200mL, or 80mL, should be the 25mg/mL standard solution, and 3/5, or 120mL, should be the water (0mg/mL).

\n" ); document.write( "ANSWER: 80mL of the 25mg/mL solution, 120mL of water

\n" ); document.write( "Finally, being a mathematician and not a pharmacologist, I prefer to solve this kind of problem with the following fast and easy informal method for finding the answer that is equivalent to the alligation method:

\n" ); document.write( "Consider the three concentrations in mg/mL on a number line: 0, 10, and 25. The 10 is 10/25 = 2/5 of the way from 0 to 25; that means 2/5 of the mixture should be the standard 25mg/mL solution. That leads quickly to the answer of 80mL of the 25mg/mL standard solution and 120mL of water.

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