#### Ex 2: Medication Dosage Calculation Using a Proportion – Two Steps

Welcome to an example of a dosage calculation that
requires multiple steps. The order is to give a patient
250 milligrams of Keflin. The bottle says to add nine
point five cc’s of sterile water to the vial to yield zero
point five grams per cc. How many cc’s will you give? To solve this problem, we’re
going to use proportions which will be formed by
setting two rates or ratios equal to each other as we see here 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 and
solve for the unknown. Notice a times d is equal to b times c. So looking at the given information, after we add the sterile water, the vial is going to yield
zero point five grams per cc. This will be our first
rate for the proportion. So zero point five grams
per cc or per one cc. Now for the second rate, we want to give the
patient 250 milligrams. So it’ll be 250 milligrams to an unknown number of cc’s, let’s call it x cc’s. But we cannot cross multiply
and solve for x in this form. Notice how we do have the
same units on the bottom, we have cc’s here and here, but on top we have grams and milligrams, which means we’ll have
to perform a conversion, either grams to milligrams
or milligrams to grams. To perform this conversion, we’ll set up a different proportion. So let’s go ahead and do that. And let’s convert grams to milligrams using our conversion here: one
gram equals 1,000 milligrams. So our proportion will
be zero point five grams is to an unknown number of milligrams, so we’ll call it y milligrams, must equal, using our conversion, one gram to 1,000 milligrams. Notice how the units are the same on the top and the bottom, so now we’ll cross
multiply and solve for y which will give us how many milligrams are in zero point five grams. When we cross multiply, we will leave off the
units to form the equation. So y times one must equal
zero point five times 1,000. Well, y times one is y, zero
point five times 1,000 is 500, and since y is equal to 500, zero point five grams is
equivalent to 500 milligrams. Which means now, in the original proportion, we can substitute 500 milligrams
for zero point five grams. So let’s go ahead and do that. Now we’re going to have 500 milligrams to one cc is equal to 250 milligrams to x cc’s. Now notice how the units are the same on the top and the bottom, milligrams, milligrams, cc’s, cc’s, and now we can cross
multiply and solve for x which will tell us how many cc’s we need. 500 times x must equal one times 250. Well 500 times x is 500x
equals one times 250 is 250, divide both sides by 500, we have x equals 250/500
which should be one half or zero point five. So to answer the question, if you need to give a patient
250 milligrams of Keflin, you need to give them
zero point five cc’s. I hope you found this explanation helpful.