Hi, this is Cathy with Level Up RN. In this video, I'll be working through a pediatric dosage calculation problem that involves calculating the safe dosage range for a child. And I'll be working through this problem on my whiteboard using three different methods including dimensional analysis, ratio and proportion, and the formula method. You can find all the information that I'll be covering in this video in our Level Up RN dosage calculation workbook. If you are in nursing school, then you know how important it is to master dosage calculations, and our workbook will help you do just that. In a nutshell, our workbook contains all different types of dosage calculation problems that you are likely to encounter in nursing school. And we demonstrate how to solve each problem using multiple methods so you can pick the way that makes the most sense to you.
So a safe dosage range is the range of doses at which the medication is effective without being toxic. So we need to get over this minimum dose to be effective, but we don't want to exceed this maximum dose because if we exceed that level, then our patient may end up with toxicity. So in this particular problem, we have an order for amoxicillin 150 milligrams PO every eight hours. Amoxicillin 125 milligrams in 5 mls of solution is available. And per the drug guide, children less than 40 kilograms receive between 20 to 40 milligrams per kilogram per day in equally divided doses every eight hours. And our child weighs 33 pounds. And we have three different questions that are being asked here. Our first question is, what is the child's weight in kilograms? So we would calculate that by taking their weight in pounds and dividing by 2.2. Or you can multiply by the correct conversion factor, which is 1 kilogram equals 2.2 pounds. So I would cross this off, and I would end up with 15 kilograms. So our patient weighs 15 kilograms, so that's the answer to part A.
Now let's work through part B of this problem. Part B is asking us what is the minimum and maximum milligrams per dose that should be prescribed based on the drug guide. So per our problem here, we are told that children should receive between 20 and 40 milligrams per kilogram per day. So over the course of a day, 20 milligrams per kilogram is the minimum dose. So if we take this and multiply it by our patient's weight, which is 15 kilograms, then we end up with 300 milligrams that the patient should receive per day. But because we are taking that dose and dividing it for administration every eight hours, that's three times per day. So I'm going to take this daily dose, divide by three, and we're going to get 100 milligrams. That is the minimum amount that we should give per dose. All right. So again, I took that daily minimum dose divided by three to get the minimum amount per dose.
Okay. What about the maximum milligrams per dose that should be given? So the maximum per the drug guide is 40 milligrams per kilogram per day. And again, I'm going to multiply by our patient's weight of 15 kilograms. And if I multiply this out, I end up with 600 milligrams. So 600 milligrams is the most that our patient should get per day. But again, since we're taking that and dividing it into three doses per day, every eight hours, I'm going to divide this by three, and that gives us 200 milligrams per dose that the patient should get. That is the maximum. So that is the answer to part B, what is the minimum and maximum milligrams? 100 is the minimum and 200 is the maximum.
All right. Part C asks us if the ordered dose is safe, how many milliliters would you administer per dose and per day? So our ordered dose is 150 milligrams every eight hours. And you can see that that falls within this safe dose range. It's over the minimum of 100 milligrams per dose, and it's under the maximum of 200 milligrams per dose. So yes, 150 milligrams every eight hours is safe. All right. So now we need to calculate how many milliliters, not milligrams, we need to administer to the patient per dose and per day. And in order to do that, I'm going to need to make some more room here, so I'm going to erase my work here. And we can solve this part of the problem with either dimensional analysis, ratio and proportion, or the formula method. So I'm going to first solve it with dimensional analysis. So our order is for 150 milligrams, and what we have available is amoxicillin 125 milligrams in 5 mls of solution. So with dimensional analysis, I'm going to multiply my ordered dose by the available concentration. And I'm going to make sure I put my milliliters on top and my milligrams on bottom such that my milligrams will cross off. And when I multiply this out, I'll be left with milliliters. So if I multiply this out, I end up with 6 milliliters. And that's how much we would give per dose.
Now, I can do the same math with ratio and proportion as well. So with ratio and proportion, I'm going to set up my ratios. On one side of the equation, I'm going to put my available concentration. That is our known ratio. And on the other side of the equation, I'm going to put our ordered dose, which is 150 milligrams, and then our unknown value as X. We're looking for the amount of milliliters it takes to give that 150 milligrams. So now I would do my cross-multiplication here. So I end up with 125 times X equals 5 times 150. Then 125X equals 750. X equals 750 divided by 125. And if you do that math, we end up with 6 milliliters. Just like we did with dimensional analysis, just an alternative way to solve that problem. So again, this is going to be per dose. And then finally, we can also solve this problem with the formula method. So using the formula method, the formula method is desired over half times the vehicle. So our desired is 150 milligrams, and what we have is 125 milligrams in 5 mls of solution. That 5 mls of solution is the vehicle that gets us that 125 milligrams. So if we do this math, again, we end up with 6 milliliters per dose. So that's the answer to how many milliliters would you administer per dose. Well, now we need to figure out how many milliliters we need to administer per day. Because we are giving this medication every eight hours, that means we are giving it three times within a 24-hour period, three times a day. So I would just take my 6 ml, multiply by three, and I get 18 mls per day that will be administered to our patient.
