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Welcome back to the RelayEd Pharmacy Techn Toolkit, a practical study newsletter designed to help pharmacy technicians and students build confidence one skill at a time.

Each issue breaks down a pharmacy concept you may see on the PTCE or encounter in practice, with clear explanations, worked examples, and quick practice to help reinforce what you learn.

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Today’s Theme: Alligation

Sometimes you need to prepare a concentration that falls between two concentrations you already have available.

Alligation gives you a quick way to determine the relative amounts of the two concentrations that should be mixed.

When can you use alligation?

Think about three numbers:

• A higher concentration
• A lower concentration
• A desired concentration somewhere between them

For example:

70% solution + 20% solution → 40% solution

Because 40% falls between 20% and 70%, alligation can be used.

Find the Ratio

Identify the three concentrations:

Higher concentration: 70%

Desired concentration: 40%

Lower concentration: 20%

Now find the difference between the desired concentration and each starting concentration:

70 − 40 = 30 parts of the lower concentration

40 − 20 = 20 parts of the higher concentration

So you need:

20 parts of 70% : 30 parts of 20%

Simplify: 2 : 3

Remember

Each difference represents the number of parts needed from the opposite starting concentration. This is the step that commonly causes errors.

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Calculation Corner: Alligation

Example 1: Finding the Amount of Each Concentration

How many milliliters of 70% and 20% solution are needed to prepare 500 mL of a 40% solution?

Step 1: Identify your values

Higher concentration = 70%

Desired concentration = 40%

Lower concentration = 20%

Step 2: Subtract to find parts

Differences:

70 − 40 = 30 parts lower

40 − 20 = 20 parts higher

Step 3: Identify the Ratio

20 parts 70% : 30 parts 20%

Simplify: 2 : 3

Step 4: Find the total number of parts

2 + 3 = 5 total parts

Step 5: Determine the amount represented by each part

500 mL ÷ 5 = 100 mL per part

Step 6: Calculate each amount

70% solution:

2 × 100 mL = 200 mL

20% solution:

3 × 100 mL = 300 mL

Answer

Mix:

200 mL of 70% solution

with

300 mL of 20% solution

to prepare 500 mL of a 40% solution.

Quick Reasonableness Check

You are making a concentration of 40%.

Because 40% is closer to 20% than it is to 70%, you should expect to use more of the 20% solution.

You do: 300 mL versus 200 mL.

That is a quick way to catch a reversed ratio.

Try It Yourself

Try this before looking below.

You have a 10% solution and a 2% solution.

How much of each should be used to prepare 400 mL of a 5% solution?

Answer

Step 1: Identify your values

Higher concentration = 10%

Desired concentration = 5%

Lower concentration = 2%

Step 2: Subtract to find parts

Differences:

10 - 5 = 5 parts lower

5 - 2 = 3 parts higher

Step 3: Identify the Ratio

3 parts 10% : 5 parts 2%

Simplify: 3:5

Step 4: Find the total number of parts

3 + 5 = 8 parts total

Step 5: Determine the amount represented by each part

400 mL ÷ 8 = 50 mL per part

Step 6: Calculate each amount

10% solution:

3 × 50 mL = 150 mL

2% solution:

5 × 50 mL = 250 mL

Answer

150 mL of the 10% solution + 250 mL of the 2% solution

Common Alligation Mistakes

Watch for these:

• Reversing which number of parts belongs to which concentration
• Forgetting to add the parts before calculating actual quantities
• Using alligation when the desired concentration is not between the two available concentrations
• Stopping after finding the ratio when the question asks for actual amounts
• Mixing units without converting them first

Watch this method on YouTube:

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Top 200 Connections: Metformin

Generic: Metformin
​Brand: Glucophage
​Class: Biguanide
​Primary use: Type 2 diabetes
​Common dosage forms: Immediate-release tablets, extended-release tablets, oral solution

What should you know?

Metformin is commonly used as part of the treatment of type 2 diabetes and works primarily by decreasing hepatic glucose production and improving insulin sensitivity.

A few high-yield points:

• GI adverse effects such as diarrhea and nausea are common, especially when starting therapy.
• Taking metformin with food may improve GI tolerability.
• Kidney function is important when determining whether metformin can be used safely.
• Long-term therapy may be associated with vitamin B12 deficiency.

Safety Check

• GI effects: Nausea, diarrhea, and abdominal discomfort are common, particularly when therapy is initiated or the dose is increased.
• Take with food: Taking metformin with meals may help reduce GI adverse effects.
• Vitamin B12: Long-term metformin use may be associated with reduced vitamin B12 levels.
• Lactic acidosis: This is rare but serious. Risk is greater in certain situations that can lead to metformin accumulation or significant physiologic stress.
• Procedures and acute illness: Metformin may need additional review around certain procedures, contrast studies, or significant acute illnesses depending on kidney function and the clinical situation.

One-Minute Knowledge Check

1.How many grams of 5% ointment and 1% ointment are needed to prepare 60 g of a 2% ointment?

A. 15 g of 5% + 45 g of 1%
B. 20 g of 5% + 40 g of 1%
C. 30 g of 5% + 30 g of 1%
D. 45 g of 5% + 15 g of 1%

2. A pharmacist needs to prepare 500 mL of a 40% solution using 50% and 10% solutions. How much of each is required?

A. 250 mL of each
B. 375 mL of 50% + 125 mL of 10%
C. 125 mL of 50% + 375 mL of 10%
D. 300 mL of 50% + 200 mL of 10%

3.A 20% ointment is mixed with an ointment base containing no active ingredient to prepare a 5% ointment. What is the ratio of 20% ointment to ointment base?

A. 1:1
B. 1:2
C. 1:3
D. 3:1

Answers below.

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Liz Fredrickson, PharmD, BCPS Founder, RelayEd liz@relayedllc.com

RelayEd provides independent educational resources and is not affiliated with, endorsed by, or sponsored by PTCB.