#### Ex 4: Medication Dosage Calculation Using a Proportion – Two Steps

Welcome to a dosage calculation, requiring multiple steps. A client weights 140 pounds. If the order is to receive a drug at the dosage of 2.5 milligrams
per kilogram of body weight, how many milligrams of the
drug will the client receive? We’re going to solve this
problem using proportions, where we set two rates or
ratios equal to each other, and as long as the units
of a and c are the same, and the units of b and d are the same, we can cross multiply, meaning a times d must equal b times c, which will allow us to
solve for the unknown. So looking at the given problem, notice how the dosage is
2.5 milligrams per kilogram, this will be our first rate, so 2.5 milligrams to one kilogram. Now the second rate involves our unknown, we want to know how many
milligrams for 140 pounds, so let’s say x milligrams,
where x is the unknown, per 140 pounds. Now it’s important that we recognize that, while we do have the same units on top, milligrams here and milligrams here, we do not have the same
units on the bottom, we have kilograms here and
pounds here, which means, we need to convert pounds to kilograms. To do this conversion, we’ll
use another proportion. To set up the conversion proportion, we’re going to use our conversion here, that 2.2 pounds equals one kilogram. So that’ll be our first ratio, 2.2 pounds is to one kilogram, as, 140 pounds is to an unknown number of
kilograms, we’ll say y kilograms. So here when we solve
for y, this will tell us, how many kilograms are in 140 pounds, which we’ll then substitute
here for 140 pounds. Also notice in this proportion, we do have the same units on top, and the same units on the bottom, so now we can go ahead and
cross multiply, and solve for y. When we cross multiply
to form the equation, we will leave off the units. So 2.2 times y, that’s 2.2y, equals, one times 140, which would be 140, and then we’ll divide both
sides by 2.2 to solve for y, let’s go and use a calculator for this, so 140 divided by 2.2, let’s go and round this
to two decimal places, we’ll say 63.64. And since y is equal to 63.64, 140 pounds is equivalent
to 63.64 kilograms, which we can now substitute here, in the original proportion. So we perform that substitution,
we’ll have 2.5 milligrams to one kilogram, must equal x milligrams to 63.64 kilograms. Now notice how the units on top, and the units on the bottom, are the same, so now we can cross
multiply and solve for x, which will tell us how many milligrams the client should receive. So we have one times x must equal 2.5 times 63.64. Well one times x of
course is just x, equals, again, 2.5 times 63.64, let’s go back to the calculator, 159.1. Remember this tells us
the number of milligrams for the patient or client
that weighs 140 pounds. So the client will receive
159.1 milligrams of medication. I hope you found this helpful.