Pharmacology math examples

Here's a typical pharmacology math problem:

1. A 30 pound Cocker Spaniel comes into your clinic needing amoxicillin for an infection. Your vet asks you to dispense the Amoxicillin based on a dosage of 11mg per kg. How much amoxicillin should the dog receive per dose?

Before getting into the problem let's approach pharmacology math by thinking about it in terms we are more familiar with. How about we temporarily change the problem as follows:
You have 30 eggs that cost $11 per dozen how much are all the eggs worth?

First, we'd figure out how many dozen we have by converting eggs to dozens of eggs. This is done by dividing the number of eggs by 12 because there are 12 eggs in a dozen. So, 30/12=2.5doz.

Since we know they cost $11 per dozen and we know we have 2.5 dozen, we just multiply 2.5x11=$27.50 right? See, you know how to do this!

With that in mind let's now attach our actual problem:

1. A 30 pound Cocker Spaniel comes into your clinic needing amoxicillin for an infection. Your vet asks you to dispense the Amoxicillin based on a dosage of 11mg per kg. How much amoxicillin should the dog receive per dose?

First you need to convert pounds to kilograms. You need to memorize the fact that there are 2.2 pounds in a kilogram. It's something you'll use a lot. So, for 30lbs you need to divide 30 by 2.2 to get 13.64kg as your answer.

This part of the problem is just like the previous problem where there were 12 eggs in a dozen. 30 eggs divided by 12 eggs per dozen was 2.5 dozen eggs.

Second part: you have a dose of 11mg per kg. You have 13.64kgs. 11mg per kg means that for every kg you need 11mg. This should tell you that you need to multiply 13.64 by 11. 13.64x11=150.04mg per dose.

This works just like the eggs costing $11 per dozen. 3 dozen would cost $33 because $11 times 3 dozen = $33.

2. The next day the owner of this Cocker Spaniel comes back to the clinic saying they can't get the dog to swallow the pills. Your vet asks that you give them liquid amoxicillin instead. The liquid you have contains 62.5mg of amoxicillin per milliliter. How many milliliters should be given per dose?

Well, we figured out before that the dosage is 150.04mg. And we have a solution that contains 62.5mg per ml or for every milliliter there are 62.5mg. So, we need to know how many 62.5's are in 150.04. We do this by dividing 150.04mg by 62.5mg and we get 2.4ml.

If you have a hard time following that we can try once again to use something more familiar to understand how to work it out: Coffee has 100mg of caffeine per cup. You need at least 300mg to get through your next Keller test. How many cups of coffee do you need? 300mg (needed) divided by 100mg (per cup) = 3 cups.

Now try a few on your own before peeking at the answers:

3. A 10lb cat comes into your clinic with a cold. The vet asks you to prepare doxycycline using 5mg per kg as the dose. How much doxycycline should be given per dose?

Invisible answer: (highlight to see)
Pound to kilogram conversion: 10lbs/2.2kg per lb = 4.5kg
Dose: 5mg x 4.5kg =22.7mg

4. You have doxycycline available in liquid form that contains 10mg per ml. How much of this solution should be given per dose?

Dose: 22.7mg/10mg per ml = 2.27ml

5. A 5lb puppy comes into your clinic and is diagnosed with roundworms. The vet asks you to draw up a dose of Strongid to give to the puppy based on 8mg/kg. The Strongid you have is 50mg/ml. How much Strongid should you prepare?

Pound to kilogram conversion: 5/2.2=2.27kg
Number of mg: 8mgx2.27kg=18.16mg
Number of ml: 18.16mg/50mg per ml=0.36ml