# Alligation Math

Alligation Math
is a method of solving a slightly complicated algebra problem. Sometimes it is called "Tic-Tac-Toe" math.

It is highly recommended to know how to perform alligations to prepare for the PTCB or ExCPT exams.

The best way to explain it is
to jump right into an example.

Q. A script calls for 25 grams of Hydrocortisone cream 15%. Your Pharmacy stocks both 5% and 20% formulations. How much of the 20% will you use in this order ?

(Attn: In the video I round numbers to the nearest quarter Gram.)

## Here's another way to do it.

Q. A script calls for 25 grams of Hydrocortisone cream 15%. Your Pharmacy stocks both 5% and 20% formulations. How much of the 20% will you use in this order ?

step-by-step

Since you have
one stronger formula and one weaker formula you can properly combine them to make your desired formula using Alligation Math.

Based on the above factors, you have three numbers to work with. The best way to get started is to draw out a
"tic-tac-toe".

1) Then, 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.

 20% 15% 5%

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.

 20% 10 15% 5% 5

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

 20% 10 Parts of the 20% 15% 5% 5 Parts of the 5%

4) Now you know that you need 15 total parts.

 20% 10 Parts of the 20% 15% 5% 5 Parts of the 5% = 15 Total Parts

5) Take the number of Parts for the first formula (the 20%) and divide it by the Total number of parts.

10 (parts) Ã· 15 (Total Parts) = .67

6)Then, take the amount of grams you need and multiply it by that.

25 Grams X .67 = 16.75 grams of the 20%

7)Then, To figure out the rest of the solution,
Simply make up the difference with the 5%

25.00 Total grams - 16.75 grams of the 20%

25.00 - 16.75 = 8.25

8.25 Grams of the 5%

 16.75 grams of the 20% Formula + 8.25 grams of the   5% Formula = 25 grams of 15% Formula

= 16.75 grams of the 20%

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