Alligation for pharmacy technicians: step-by-step with worked examples
Alligation answers a common compounding question: how much of a higher strength and a lower strength do you mix to make a target strength? The tic-tac-toe grid is just a way to organise one subtraction per ingredient.
Method
- Write the higher strength top-left, the lower strength bottom-left, and the desired strength in the middle.
- Parts of the higher strength = desired − lower.
- Parts of the lower strength = higher − desired.
- Add the parts. Each ingredient's share of the total is its parts ÷ total parts.
- Multiply each share by the total amount you need.
Worked examples
Example 1
How many grams of 25% ointment must be mixed with 0.5% ointment base to make 200 g of 12.5% ointment? Round to one decimal place.
Show solution
- Parts of 25% = desired − low = 12.5 − 0.5 = 12
- Parts of 0.5% = high − desired = 25 − 12.5 = 12.5
- Total parts = 24.5
- Grams of 25% = 200 g × 12/24.5 = 97.9592 g, which rounds to 98 g
Answer: 98 g
Example 2
How many grams of 10% ointment must be mixed with 1% ointment base to make 100 g of 5% ointment? Round to one decimal place.
Show solution
- Parts of 10% = desired − low = 5 − 1 = 4
- Parts of 1% = high − desired = 10 − 5 = 5
- Total parts = 9
- Grams of 10% = 100 g × 4/9 = 44.4444 g, which rounds to 44.4 g
Answer: 44.4 g
Example 3
How many grams of 20% ointment must be mixed with 0.5% ointment base to make 100 g of 10% ointment? Round to one decimal place.
Show solution
- Parts of 20% = desired − low = 10 − 0.5 = 9.5
- Parts of 0.5% = high − desired = 20 − 10 = 10
- Total parts = 19.5
- Grams of 20% = 100 g × 9.5/19.5 = 48.7179 g, which rounds to 48.7 g
Answer: 48.7 g
Tips
- A diluent or base counts as 0%.
- The desired strength must lie between the two strengths you have, or it cannot be made.
- Check: (amount × strength) for both parts should add up to (total × desired).
Practise with unlimited problems like these
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