Question

A doctor needs to administer 2 mL of a 100 mg/mL solution to a 200 lb. patient. However, the doctor has the solution available only in 20 mg/mL strength. What volume of the 20 mg/mL solution would be needed to administer the desired dose?

A. 30 mL
B. 40 mL
C. 20 mL
D. 10 mL

Answer 1

To deliver an equivalent dose using a 20 mg/mL solution, a doctor needs to administer 10 mL of this solution to provide the same amount of medication as 2 mL of a 100 mg/mL solution. The correct option is D. 10 mL.

Step-by-step explanation:

The question revolves around the concept of dilution and concentration of medical solutions, which requires the use of basic mathematical skills to determine the volume of a 20 mg/mL solution needed to achieve the same dosage as 2 mL of a 100 mg/mL solution. To solve this, we set up a proportional relationship because the amount of the drug to be administered stays constant.

The original prescribed dosage is:

• 2 mL of a 100 mg/mL solution

This means the total amount of the drug to be administered is:

2 mL × 100 mg/mL = 200 mg

Using the 20 mg/mL solution, we need to find the volume (V) that contains 200 mg of the drug:

20 mg/mL × V = 200 mg

Solving for V, we get:

V = 200 mg / 20 mg/mL

V = 10 mL

Therefore, the doctor needs to administer 10 mL of the 20 mg/mL solution to deliver the same amount of medication as 2 mL of the 100 mg/mL solution. The mention correct option for the needed volume of the 20 mg/mL solution is D. 10 mL.