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Prescription Calculation

by Scarlett
(Studying at home)

A prescribed drug is available as a 20% solution.
The patient weights 97lbs, and has been ordered to take 40mg/kg q6h x 10 days. If the solution is packaged in 6 fl. oz. bottles, how many will be required for this order?

Please show your work.

Comments for Prescription Calculation

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Dimensional analysis method
by: Brad Wojcik, Pharm D

This is a good example of how you can do a complicated problem all in one step using dimensional analysis. You have to come up with some of your own ratios from the info provided. The 40 mg/kg is the amount per dose, so you can write 40mg/kg*dose. q6h is 4 doses/day. The 10 days is actually 10 days/course. The way I did it was just wrote down 97 lbs and started adding ratios until I got to bottles. I changed 20% to 20g/100mL, but you could also use 20%g/mL.
97lb(1kg/2.2lb)(40mg/kg*dose)(4dose/day)(10days/course)(100mL/20g)(1g/1000mg)(1 oz/30mL)(1 bottle/6 oz)= 1.96 bottle/course, so you would need 2. These seems complicated, but if you learn this method it is easy to do these problems.

hard
by: Anonymous

I find this hard ! is there a easier way ?

reply to too hard
by: Brad Wojcik, Pharm D

Hello.It might be easier to break the problem up into smaller problems. If you prefer ratio proportion, you can do each of these steps using that method.
1) Change 97 lb to kg. 97 lb(1 kg/2.2 lb)= 44 kg
2) Calculate how many mg per dose. 44 kg(40mg/kg)= 1760 mg.
3) At this point chang 1760 mg to g. 1760 mg(1g/1000mg)= 1.76 g
4) Calculate how many doses you will need. You will need 4 doses per day for 10 days, which is 40 doses.
5)Calculate how many grams you will need for the 40 doses. 40 doses (1.76g/dose)= 70.4 g
6)The 20% solution means 20g/100mL. Calculate how many mL you will need for the 70.4 g. 70.4 g(100mL/20g)= 352 mL
7) Change 352 mL into fl oz. We will use 30 mL/fl oz. 352 mL(1 fl oz/30 mL)= 11.7 fl oz.
8) Change 11.7 fl oz into bottles. 11.7 fl oz(1 bottle/6 fl oz)= 1.95 bottles, so you would need 2 bottles. Each of these problems can be solved using ratio proportion. Step 1 would be done like this. x kg/97 lb = 1 kg/2.2 lb solving for x kg you get 44.09 kg. Either way, this problem has a lot of steps.

RX Calculation
by: Ri

391ml?
sol.
97lbs/2.2kg=44kg*40mg*4*10= 70,400/180ml=391ml
is this correct?

Reply to Ri
by: Brad Wojcik, Pharm D

391ml?
sol.
97lbs/2.2kg=44kg*40mg*4*10= 70,400/180ml=391ml
is this correct?

No. To begin with you have to have units on all of your calculations. The first step is not dividing 97 lb by 2.2 kg, it is multiplying 97 lb by (1 kg/2.2 lb). This way lb cancel out and you are left with kg. Also, you don't divide by 180 ml in any of the steps.All of the steps are in the previous post. If you watch my videos on youtube you will see how to do these calculations step by step. Just google Dr. Brad and Pharmacy Calculations and you should be able to find them. Also, you can email me at brad.wojcik@gmail.com and I can help you on specific problems.


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