Alligation Math
Example




Question from Quiz #5, Question #4 :

You have been asked by the pharmacist to prepare 3 liters of a 30% strength solution. Your pharmacy stocks the active ingredient in 8 ounce bottles of 70% strength. How many bottles of the active ingredient will you need to open to complete this request?


This question involves 3 calculations. The first is figuring out how much of the active ingredient you need in ml. The second is, based on the first calculation, how many ounces will be needed to supply that much of the active ingredient. Then how many 8oz bottles will accommodate that request.

The first part can be solved using
Alligation Math.

Here's how:

Based on the factors in the question:

1) You have 70% concentration to work with.
2) You have 0% concentration to work with.(NS or Water, etc.)
3) Your order is for 3000ml of 30% solution.


The best way to get started is to draw out your
"tic-tac-toe".

1) Take the two formulas you have and place them in the top left and bottom left positions and your desired formula in the center of the Tic Tac Toe.

70%      
30%
0%






2) Now, do two diagonal subtractions to get the difference between what you have and what you want and write the answers in the right hand top and bottom. You will have one negative number, but always write it as positive.

70% 30  
30
0% 40  






3) What you have done is determine how many parts of each formula to use to arrive at the desired formula.

70% 30 Parts of the 70%  
30%
0% 40 Parts of the 0%  






4) To make things easier, go ahead and reduce that fraction down to its lowest form.

30 Parts of 70%  
   →    
3 Parts of 70%

       

40 Parts of 0%  
   →    
4 Parts of 3%






5) Now you know that you need 7 total parts.

70% 3 Parts of the 70%  
30%
0% 4 Parts of the 0%  
=
7 Total Parts  






6) Now use proportions math to calculate how much 3 parts would equal.

7 Parts
       
3 Parts

       

3000mL
       
1286mL





7) So, now the question becomes, how many Ounces will you need to open to get 1286ml. This is a simple conversion.

1oz
       
43oz

       

30mL
       
1286mL


8) Lastly, how many 8oz bottles will you need to open to get 43oz.

43 ÷ 8 = 5.38

Which means you would need to open 6 Bottles





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