Using units to solve problems: Drug dosage

I just received this drug calculation problem from a nursing student and I think it's essential that the nursing students out there are able to do this just in case I'm the patient receiving the drug so let's do it and I think it's a it's an interesting unit conversion problem for pretty much anyone who wants practice with unit conversion so the question is that we have a doctor the doctor orders orders drug X drug X and this is the dosage that the doctors requesting they're saying five milligrams five milligrams of our drug per pound of patient weight for others right per pound of patient weight every 12 hours this is what we're supposed to do but our supply of the drug our supply right here our supply in green it isn't just you know step not just nuggets in milligrams it's a solution there's a certain amount of grams for every milliliter that we have of the solution it's dissolved and some maybe probably some water so this is our supply of drug X drug X every we have 0.9 I'll write a zero in front my wife who is a doctor says it's essential to write the zero and from the decimal we have 0.9 grams per milliliter milliliter of solution so if I were to take one milliliter out of my solution and give it to someone I'm essentially giving them point nine grams of this drug and then the final piece of information we're given the final piece of information we're given is that the patient the patient they weigh and we should say they mask as kilograms is mass but we get the idea the patient is seventy two point seven kilograms seventy two point seven kilograms so there's a couple of interesting things here we have to figure out the dosage in terms of milliliters we have to oh actually I even tell you the question we have to say the question is how many milliliters of solution do we have to give to the parent perd to the patient per dose so milliliters of solution per dose that's our question and there's a couple of things we have to go from milligrams to grams and then convert that to milliliters and then they tell us per pound but then they gave us the patient's weight or their mass and kilograms you have to do some conversion there so I I definitely can appreciate how this can be a little daunting and maybe confusing a time so let's just do it step by step so the first interesting thing and this is just something that you might need to know or you might have written down on paper or a you might have a calculator that does this it's just how to convert kilograms to pounds and it's it's good to know in general if you're converting between the metric and the English systems so one kilogram is approximately equal to 2.2 pounds not exactly but that's a pretty good approximation and one pound if you just take one over that one pound is approximately equal to 0.45 0.45 kilograms so we'll just put this in a box this is the only kind of outside conversion information we'll need to do this problem everything else we'll just need a calculator unless we just want to spend a lot of time doing some arithmetic so the first thing let's let's figure out our dosage in terms of per kilogram this is per pound and we really don't need to know every 12 hours because they're saying how much how many milliliters of solution do we do per dose a dose is every 12 hours so we just really you know they every 12 hours it's kind of extra information so we want to figure out this five milligrams per pound how do we convert that to how many milligrams per kilogram so let's do five I'll write it down here in magenta five milligrams per pound and then we want to convert this to per kilogram so we could multiply this times the number of pounds per kilogram times I'll do it in yellow times this information right up here times two point two pounds pounds per kilogram and if you ever get confused you know jihad it's a low two x two point two instead of dividing by two point two which is the same thing as multiplying by point five you can pay very close attention to the units notice how about 2.2 pounds per kilogram 2.2 pounds per 1 kilogram and you'll know this this will work out because you have a pound in the numerator and you have a pound in the denominator that's called dimensional analysis but it's a very you know if you ever get confused with these things and I think when you once you do enough practice you'll find that you won't have to pay too much attention to this but at first when you're getting started just to make sure you're not you know multiplying or dividing by the wrong thing just make sure the dimensions cancel out pounds in the numerator pounds in the denominator so let's do that pounds in the numerator pounds of the denominator cancel out and you multiply 5 times 2.25 point times two point two this is equal to this is equal to see five times two is 10 5 times 0.2 is 1 so this is equal to 11 and then in our numerator we have milligrams 11 milligrams per kilogram so we've just converted our our dosage information to a pure metric system I was actually a mix between the metric and the English system before now let's see what we can do well let's see if we can get it in terms of how many milliliters we have to deliver per pound so once again we want this well actually let's go to grams first because we have milligrams here we have grams up here so let's see if we can convert this thing to grams so just like we did before we want a milligrams in the denominator I'll do it in orange we want a milligrams in the denominator and we want to gram in the numerator why did I say that because I want this and this to cancel out and I want two grams in the numerator so how many grams are there per milligram you can just think it through there's one gram per thousand milligrams or 1000 milligrams per gram and you just multiply it out so the milligrams cancels with the milligrams and then we get this is equal to 11 over 1,000 grams per kilogram four kilograms so now we have everything in terms of grams but we wanted in terms of milliliters the question is how many milliliters of solution per dose so let me go down here on this line right here so we had what we had this this result we have 11 over 1000 I won't do the division just yet grams of our of drug X per kilogram this is just this is really just a re we've just rewritten this dosage information in different units and let's see how much solution we need per kilogram so what I want I want to cancel out the grams here and have a milliliters there so to cancel out that grams I'm going to have to have a gram in the denominator and a milliliter in the numerator in a milliliter milliliter in the numerator so in our solution how many grams are there per milliliter well they told us there's 0.9 grams per milliliter or for every one milliliter there are point nine grams notice I just took the inverse of that because we want a milliliter in the numerator grams in the denominator so that these two cancel out and let's do this multiplication now so our grams cancel out we have milliliters per kilogram milliliters per kilogram and then we multiply that 11 over a thousand times the one over 0.9 so I'll just keep let me just write it like this so this is going to be 11 over 1,000 times 0.9 times 0.9 milliliters of our solution per kilogram so we've gotten this far so this per kilogram of patient body weight and then finally they tell us how many kilograms our patient weighs so let's do that last multiplication that we can actually get our calculator out and do it all at once so let's multiply this times we want to know how many milliliters per patient we want the kilograms to cancel out so we want kilograms per patient and we're talking about this particular patient not every patient is going to be the same number of kilograms but if we do this kilograms will cancel out we'll have milliliters per page milliliters of solution per patient which is exactly what we want we want milliliters of solution per dose per patient but where everything we've assumed so far has been per dose so how many kilograms is a patient way well there's 72 72.7 kilograms per patient that's how much the patient weighs so we just do this final multiplication and we'll be done so our answer and as these two things are going to cancel out so our final answer is going to be 11 times 72 point 7 divided by 100 times actually a hundred times 0.9 is pretty easy to figure out that's nine hundred divided by nine hundred milliliters per patient or you could just say milliliters per dose however you want to say per dose per patient so let's get our calculator out and do this so we have 11 times 72 point seven is equal to 799 divided by nine hundred is equal to 0.88 well we could round up point eight eight nine hopefully the doctor won't mind so that is equal to this is equal twelve right in a nice vibrant color zero point eight eight nine milliliters of solution of solution per dose so this is what we're going to give every 12 hours if they ask how many total milliliters over the course of two days we would have to say oh there's 48 hours we'd multiply it by four but that twelve hours was extra information in this problem but anyway hopefully this is hopeful this is useful and it will Mittal help ensure that any nurses serving me in the future are are giving me my proper dosage and hopefully I get the doctor even got the right dosage to the right to begin with because otherwise it's all for naught anyway