Question

a pharmacy technician is preparing a prescription for a mouthwash that contains a 1:2:1 ratio of diphenhydramine, lidocaine, and aluminum hydroxide. if the solution contains 60 ml of lidocaine, how many ml of diphenhydramine should the technician compound?
30 ml
15 ml
60 ml
20 ml

Explanation:

Step1: Understand the ratio

The ratio of diphenhydramine : lidocaine : aluminum hydroxide is \(1:2:1\). Let the volume of diphenhydramine be \(x\), lidocaine be \(2x\), and aluminum hydroxide be \(x\) (since the ratio parts are 1, 2, 1 respectively).

Step2: Use lidocaine volume to find \(x\)

We know the volume of lidocaine is \(60\) mL, and from the ratio, lidocaine is \(2x\). So we set up the equation \(2x = 60\).
To find \(x\), we solve for \(x\) by dividing both sides of the equation by 2: \(x=\frac{60}{2}=30\). Since \(x\) is the volume of diphenhydramine, the volume of diphenhydramine is \(30\) mL.

Answer:

30 mL