Calculus help?!

Question

The blood serum concentration of the antibacterial drug ciprofloxacin increases proportionately with the dose of drug administered. If a 250 mg dose of the drug results in a serum concentration of 1.2 micrograms of drug per milliliter of serum, how many micrograms of drug would be expected per milliliter of serum following a dose of 500 mg of drug?

Answer 1

Luckily this problem does NOT require calculus...just some proportions! Proportions are helpful and are common in pharmacology. Here is a basic blueprint of what it looks like to set up an equation with proportions:

A / B = C / D

then crossmultiply

B x C = A x D

A and C, the numerators, must share the same unit of measure. B and D, then denominators, must share the same unit of measure. As long as you only have one unknown variable, you can solve it.

For this problem, we have 250 mg drug corresponding to a 1.2 microgram/mL serum level, and we have a 500 mg drug corresponding to an unknown serum level. Because it rises proportionally, we can set up an equation of proportions:

250 mg / 1.2 micrograms per mL = 500 mg / X micrograms per mL

Notice how the top numbers are both mg of drug, and the bottom are both micrograms per mL, the units of measure must match. Now we cross multiply:

(1.2 )(500) = (250)(X)

Now do your math to simplify and isolate X (get it alone on one side of the equation)