Pharmacy Math alligation
Alligation Math

Here is a step-by-step example of a
Pharmacy Math alligation.

Question from Wayne in California:

If a physician orders 25% dextrose 1000mL and all you have is a Liter of 70% dextrose, how much 70% dextrose and how much sterile water will be used ?

This question is worded to attempt to trick you into thinking it's a Proportion equation. However, you would want to use
Pharmacy Math alligation to quickly solve it.

Here's how:

Based on the factors in the question, you have three numbers to work with.

1) You have 70% Dextrose to work with.
2) You have Sterile water to work with (0%).
3) Your order is for 1000mL of 25% Dextrose.

The best way to get started is to draw out a

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.


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

70% 25  
0% 45  

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

70% 25 Parts of the 70%  
00% 45 Parts of the 00%  

4) Looking at the "Parts", you see that we get 25:45. To make things easier, go ahead and reduce that fraction down to its lowest form..

25 Parts of 70%  
5 Parts of 70%


45 Parts of 00%  
9 Parts of 00%

5) Now you know that you need 14 total parts.

70% 5 Parts of the 70%  
00% 9 Parts of the 00%  
14 Total Parts  

6) Take the number of Parts for the first formula (the 70%) and divide it by the total number of parts.

5 parts ÷ 14 Total Parts = .36

Then, take the amount of milliliters you need and multiply it by that.

X .36
= 360ml

(of the 70%)

7) Then, to figure out the rest of the solution,
make up the difference with the other parts (the 00%)

1000 Total ml
- 360ml (of the 70%)
= 640ml

(of the 00% / Sterile Water)


360 Milliliters of the 70% Dextrose
640 Milliliters of the sterile water
1000 Milliliters of 25% Dextrose

This is how it might look on the Exam:

If a physician orders 25% dextrose 1000ml and all you have is a Liter of 70% dextrose, how much 70% dextrose and how much sterile water will be used ?

A. 750ml of 70% / 250ml Sterile Water

B. 440ml of 70% / 560ml Sterile Water

C. 360ml of 70% / 640ml Sterile Water

D. 250ml of 70% / 750ml Sterile Water

Correct Answer is c

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