Analyzing a Prescription for the Correct Dose

Date: 04/27/2005 at 12:24:46
From: Alicia
Subject: Converting tsp. to ml

1 Tsp of Proventil syrup is ordered three times a day for a 5 year old
child with asthma.  It is supplied as 2mg/5ml.

How much Proventil is he getting per dose? 

A safe starting dose is 0.1 mg/kg (of weight) three times a day.  The
child weighs 46 pounds.  Is the prescribed dosage safe?

Date: 04/28/2005 at 15:31:43
From: Doctor Wilko
Subject: Re: Converting tsp. to ml

Hi Alicia,

Thanks for writing to Dr. Math!

To find the conversions, I went to www.google.com and typed:

  "1 Tsp = ? ml"

and

  "1 lb = ? kg"

Google gave the answers as:

  1 US Tsp = 4.92892161 ml  (or about 5 ml)

and

  1 lb = 0.45359237 kg  

It looks like I'm ready to start solving my problem!

Before I start trying to do the math, I want to read back through the 
problem and make sure I understand everything.

   1 Tsp of Proventil syrup is ordered three times a day for a 5 year
   old child with asthma.

The age and asthma aren't really important, just 1 Tsp three times a
day.  Good so far?

  It is supplied as 2mg/5ml.

For every 5 ml of the syrup, the patient will get 2 mg of the actual 
medicine.  Do you agree?

  How much Proventil is he getting per dose?

From Google, I found that 1 Tsp is about 5 ml. It was given that each 
5 ml of syrup delivers 2 mg of medicine, so the patient is getting 2 
mg of Proventil _per dose_ (because one dose is one Tsp, which is 5 
ml).

  A safe starting does is 0.1 mg/kg (of weight) three times a day. The
  child weighs 46 pounds. Is the prescribed dosage safe?

You were given that a safe dose is 0.1 mg of medicine for every 1 kg 
of body weight.  It was given that the patient weighs 46 lbs.  First 
thing is to convert pounds (lb) to kilograms (kg):

  1 lb = 0.4536 kg (approximately), so therefore

  46 lbs = 46 * 0.4536 or 20.8652 kg

A safe dose is 0.1 mg of medicine for every 1 kg of body weight, so a 
safe dose for this specific 46 lb (20.8652 kg) patient is:

  0.1 mg    20.8652 kg
 -------- * ---------- = 2.0865 mg (per dose)
  1 kg          1

Since the patient is getting 2 mg of medicine per dose, it looks like 
the prescribed dosage is safe because it's within limits (from the 
conversion above, the patient could receive up to 2.0865 mg of 
medicine per dose and still be safe).

The main thing with these types of problems is making sure you 
understand exactly what's being asked and getting the proper 
conversions _before_ you start trying to solve the problem.  Even if 
the problem sounds wordy or like it has a lot of math, if you break it
down line by line like I did above, you'll find that the problem
becomes much more manageable.

Does this help?  Please write back if you have further questions.

- Doctor Wilko, The Math Forum
  http://mathforum.org/dr.math/