Question 1195880: Alligation method
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?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39626)   (Show Source):
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
The response from the other tutor shows a standard algebraic method for solving the problem.
If you actually want to solve the problem using the alligation method, then it might look something like this:
25 10 (=10-0)
\ /
10
/ \
0 15 (=25-10)
The 25 and 0 at the left are the concentrations in mg/mL of the two ingredients.
The 10 in the middle is the desired concentration.
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.)
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).
ANSWER: 80mL of the 25mg/mL solution, 120mL of water
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:
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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