Pharmacy Calculations: Alligations - PTCB Math Pharmacy Technician CPhT Test Prep Alligation Method
Summary
This video explains the pharmacy calculation method called allegation, used to determine the amounts of two different drug concentrations needed to create a desired concentration. It details two methods for solving allegation problems: the ratio method and the tic-tac-toe method. Both methods involve identifying high, low, and desired concentrations, calculating ratios or differences, summing parts, and then multiplying by the total quantity required to find the specific amounts of each concentration to be mixed. An example is provided for each method, demonstrating how to calculate the correct volumes for compounding.
Key Insights
Key characteristics of allegation problems include two available concentrations and a different required concentration.
To recognize an allegation calculation problem, there are two main criteria: first, there will be two different concentrations or strengths of the same drug available, and second, a different concentration is required to be made from those two available concentrations. One of the available concentrations will always be stronger and the other weaker than the desired concentration.
Allegation provides a systematic approach to solving complex compounding mixture problems.
Allegation is a structured method designed specifically for solving problems where two known concentrations of the same drug are mixed to create a desired concentration. It simplifies the process of determining the precise quantities of each component needed, ensuring accuracy in pharmaceutical compounding.
Sections
Introduction to Allegation
Allegation is a method to calculate the amounts of two same-drug concentrations needed to achieve a different concentration.
Allegation is a method for calculating the amounts of two concentrations of the same drug that are needed to make a different concentration from what is available. It can be used for various products like liquids and creams and is particularly useful in compounding.
An example problem involves mixing 50% and 10% solutions to create 20% solution.
The example problem presented is: a prescription requires 100 ml of a 20% solution. The pharmacist has 50% and 10% solutions in stock. The question is how much of each solution should be mixed to make the required 100 ml of 20% solution.
Key characteristics of allegation problems include two available concentrations and a different required concentration.
To recognize an allegation calculation problem, there are two main criteria: first, there will be two different concentrations or strengths of the same drug available, and second, a different concentration is required to be made from those two available concentrations. One of the available concentrations will always be stronger and the other weaker than the desired concentration.
Two methods exist for solving allegation calculations: the ratio method and the tic-tac-toe method.
There are two primary methods for solving allegation calculations: the ratio method and the tic-tac-toe method. The video will cover both, allowing the user to choose the one that is easiest for them to understand and apply.
The Allegation Ratio Method
Steps for the ratio method: identify concentrations, subtract to find ratio, sum parts, then set up and multiply fractions.
The ratio method involves four main steps. Step one: identify the high concentration (HC), low concentration (LC), and desired concentration (DC). Step two: subtract to obtain the ratio of HC to LC; the DC minus LC gives the HC ratio value, and HC minus DC gives the LC ratio value. Step three: add the HC ratio value and LC ratio value to determine the total number of parts. Step four: set up fractions using these parts and multiply by the total quantity needed to find the amount of each concentration required.
Applying the ratio method to the example: 25 ml of 50% and 75 ml of 10% are needed.
Using the example (100 ml of 20% solution needed, from 50% and 10% stock), the steps are: HC=50, LC=10, DC=20. DC-LC = 20-10 = 10 (HC ratio value). HC-DC = 50-20 = 30 (LC ratio value). The ratio is 10:30, or 1:3. Total parts = 1 + 3 = 4. For HC (50%): (1/4) * 100 ml = 25 ml. For LC (10%): (3/4) * 100 ml = 75 ml. The total volume is 25ml + 75ml = 100ml.
The Allegation Tic-Tac-Toe Method
The tic-tac-toe method involves setting up a grid and calculating differences diagonally.
The tic-tac-toe method starts by placing the high concentration (HC) in the top left, the desired concentration (DC) in the center, and the low concentration (LC) in the bottom left of a tic-tac-toe grid. Then, differences are calculated diagonally: HC minus DC goes in the bottom right, and DC minus LC goes in the top right.
Total parts are found by adding the diagonal differences vertically; fractions are then derived for each concentration.
After placing the diagonal differences (HC-DC and DC-LC) in the grid, these two numbers are added vertically to find the total parts. The fraction for the high concentration is the number in the top right (DC-LC difference) divided by the total parts. The fraction for the low concentration is the number in the bottom right (HC-DC difference) divided by the total parts.
Applying tic-tac-toe to the example: results match the ratio method, yielding 25 ml of 50% and 75 ml of 10%.
Using the same example (100 ml of 20% from 50% and 10%), set up the grid: HC=50 (top left), DC=20 (center), LC=10 (bottom left). Diagonal calculations: 50-20 = 30 (bottom right), 20-10 = 10 (top right). Total parts = 30 + 10 = 40. HC fraction = 10/40. LC fraction = 30/40. Multiply by quantity needed (100 ml): HC = (10/40) * 100 ml = 25 ml. LC = (30/40) * 100 ml = 75 ml. This yields the same result as the ratio method.
Allegation provides a systematic approach to solving complex compounding mixture problems.
Allegation is a structured method designed specifically for solving problems where two known concentrations of the same drug are mixed to create a desired concentration. It simplifies the process of determining the precise quantities of each component needed, ensuring accuracy in pharmaceutical compounding.
Summary and Key Takeaways
Allegation is for mixing two concentrations to achieve a desired concentration.
Allegation is a method for calculating the amounts of two concentrations from the same drugs needed to make a different concentration from what's available. One concentration is higher (HC) and one is lower (LC) than the desired concentration (DC).
Both ratio and tic-tac-toe methods yield correct results for allegation problems.
The ratio method and the tic-tac-toe method are both valid ways to determine the amounts of the high and low concentration solutions needed to make the desired concentration. Users should choose the method that makes the most sense to them.
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