Pharmacy Alligation / tic-tac-toe math

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Tic-Tac-Toe Math
Example

Tic-Tac-Toe math refers to Alligation Math.

Question from Malibu : from the ask a question page

HOW MANY MILLILITERS OF 50% DEXTROSE SOLUTION AND HOW MANY MILLILITERS OF 5% DEXTROSE SOLUTION ARE REQUIRED TO PREPARE 4500mL OF A 10% DEXTROSE SOLUTION ? CAN YOU PLEASE DO OUT THE WHOLE EQUATION STEP BY STEP FOR ME THANK YOU?

This can be solved using an Alligation / Tic-Tac-Toe Math.

Here's how:

Based on the factors in the question:

1) You have 50% Dextrose to work with.
2) You have 5% Dextrose to work with.
3) Your order is for 4500mL of 10% Dextrose.

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.

50%
	10%
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.

50		5
	10
5%		40

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

50%		5 Parts of the 50%
	10%
5%		40 Parts of the 5%

4) To make things easier, go ahead and reduce your parts down to lower terms. (since you can)..

~~5 Parts of 50%~~	→	1 Part of 50%

~~40 Parts of 5%~~	→	8 Parts of 5%

5) Now you know that you need 9 total parts.

50%		1 Part of the 50%
	10%
5%		8 Parts of the 5%
	=	9 Total Parts

6) Now use proportions math to calculate how much 1 part would equal.

9 Parts		1 Part

4500mL		500mL

7) Then, to figure out the rest of the solution,
simply make up the difference with the other parts (the 5%).

4500 Total Ml
- 500mL (of the 50%)
---------
= 4000mL(of the 5% )

Cross check

4000 Milliliters

of the 5% Dextrose

+500 Milliliters

of the 50% Dextrose

4500 Milliliters

of 10% Dextrose

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