Question

A doctor prescribes an ointment that is 2% hydrocortisone. A pharmacist has 1% and 5% concentrations in stock. How many ounces of each should the pharmacist use to make a 7-ounce tube?

Answer 1

We need to find the number of ounces of 1% hydrocortisone and 5% hydrocortisone the pharmacist should use to make a 7-ounce tube with a concentration of 2% hydrocortisone.

Let's call x the number of ounces of 1% hydrocortisone, and y the number of ounces of 5% hydrocortisone.

Then, 1% of x added to 5% of y must result in 2% of 7:

$\begin{gathered} 1\%\cdot x+5\%\cdot y=2\%\cdot7 \\ \\ 0.01x+0.05y=0.02\cdot7 \\ 0.01x+0.05y=0.14 \end{gathered}$

Also, we have:

$\begin{gathered} x+y=7 \\ \\ \Rightarrow y=7-x \end{gathered}$

Then, using the above result in the first equation, we obtain:

$\begin{gathered} 0.01x+0.05(7-x)=0.14 \\ \\ 0.01x+0.35-0.05x=0.14 \\ \\ -0.04x+0.35=0.14 \\ \\ -0.04x=0.14-0.35 \\ \\ -0.04x=-0.21 \\ \\ x=\frac{-0.21}{-0.04} \\ \\ x=5.25 \end{gathered}$

Now, using this result back in the second equation, we obtain:

$y=7-5.25=1.75$

Therefore, the answers are: