The alligation method is a powerful approach to solving dilution and concentration calculations questions. But when is it better to use the alligation approach as opposed to the algebraic method? Before I tell you, let us take a look at this interesting concentration questions and see how it illustrates an important concept regarding when it is better to use the alligation method.
Question
You receive a prescription for 60 grams of a 2% w/w voltaren gel. How many grams each of a 5% w/w voltaren gel and gel base must be used to fill this prescription?
Analysis of the Question using Alligation Method
Notice that in the question you are actually compounding a 2% w/w gel and you are using two components. You are combining a 5% w/w voltaren gel and a gel base.
First, it is important to understand that the gel base has no active ingredient and so its concentration is zero percent (0% w/w).
Now, there are two ways you can solve this problem. You can use the algebraic approach (C1Q1 +C2Q2 = CfQf ; where C1 and Q1 are concentration and quantity of first ingredient, respectively, C2 and Q2 are concentration and quantity of second ingredient, respectively, and Cf and Qf are concentration and quantity of final product, respectively) or you could solve this question using alligation method.
For these types of problems where you have two concentrations and the desired concentration falls between the two concentrations, the alligation approach actually works better than the algebraic method. It is typically faster.
Solution
If you need a more extensive review on the alligation method check my alligation video.
However, let’s get right to the solution. See step-by-step solution in the video and keep reading.
The first step is to set up the alligation grid.
So once you have your grid set up, the highest strength (5%) goes to the top left and then what goes to the bottom left is the lowest strength (0%) and in the middle you have the desired strength and in this case it's 2%.
Now the way alligation setup works is we want to find out what the number of parts of the gel base is going to be. So we will subtract the 2% which is the desired from the 5% (higher strength) and that gives us 3 which goes to the bottom right.
This 3 actually represents the number of parts of the gel base (0%), so we have three parts of the gel base.
We do a similar thing for the parts of the highest strength (5%). So we subtract the 0 from 2
and that gives us 2 and that goes to the top right of the grid.
We now have 2 parts of the 5% and 3 parts of the gel base (0%) which gives us a total of five parts.
Quantity of the 5% w/w Voltaren Gel Required
So to determine how much we will need of the 5% w/w voltaren gel, we will take the parts of the 5% which is 2 and divide that by the total parts which is 5 and then multiply that result by the total quantity we are making which is 60 grams. So when we do the math we would need 24 grams of the 5% w/w voltaren gel.
Quantity of the gel base Required
Now to figure out how much of the gel base we need, we could do that in two ways. We can repeat the process above. In which case we will take the parts of the gel base which is 3 and divide that by the total parts which is 5 and then multiply the result by the total quantity which again is 60 grams and that should give us 36 grams.
However there's a much quicker way. What we could do instead is take the total quantity that we are preparing which in this case is 60 grams and because there are only two components, we will subtract the quantity of the 5% which we already determined to be 24 grams and that should still give us 36 grams.
Whenever you have a concentration calculation problem where you have two different strengths and your desired strength falls between those two concentrations, it is often better to use the alligation method rather than the algebraic method. The alligation method tends to be faster in those cases.
Take home message: So the answer to the question in the first paragraph is whenever you have a concentration calculation problem where you have two different strengths and your desired strength falls between those two concentrations, it is often better to use the alligation method rather than the algebraic method. The alligation method tends to be faster in those cases.
When else is better to use the alligation method instead of the algebraic approach to solve concentration calculations questions? Tell us about it by leaving a comment. Also, feel free to share any other great ideas too.
