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

Each issue works through a practical pharmacy skill, often through a calculation you may encounter on exams, during laboratory activities, or on rotations, and pairs it with the clinical reasoning behind the numbers.

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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 300 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

• Kidney function: Check renal function when starting and monitoring metformin. Metformin is contraindicated when eGFR is below 30 mL/min/1.73 m², and starting therapy is generally not recommended when eGFR is 30–45 mL/min/1.73 m²
• 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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Industry Fellowship Toolkit

Interested in pharmaceutical industry but unsure what the fellowship process actually involves?

The Industry Fellowship Toolkit is designed to support pharmacy students and pharmacists interested in fellowship opportunities and careers in industry.

Use it as a starting point to better understand the pathway, organize your preparation, and approach the fellowship process with more direction.

Whether you're actively applying or simply exploring industry as a possible career path, the toolkit can help you learn what the process looks like and what to consider along the way.

Explore the Industry Fellowship Toolkit

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

RelayEd provides independent educational resources and is not affiliated with, endorsed by, or sponsored by NABP or USP. NAPLEX® is a registered trademark of the National Association of Boards of Pharmacy. USP® is a registered trademark of the United States Pharmacopeial Convention. Always verify medication information using current product labeling, course materials, and workplace policies.