Drug Prescription: Understanding Dosage Calculation

Accurate drug dosage calculation is a critical skill in healthcare, ensuring patient safety and effective treatment. This problem requires us to determine the volume (in ml) of a drug to be administered, given a specific prescription and the available concentration of the drug.

Prescription Details for Drug Administration

Let's first identify the given information:

• Prescribed Dose: The amount of drug ordered by the doctor. In this case, it is \(20 \, \text{mcg}\).
• Available Dose: The concentration of the drug as supplied. Here, it is \(30 \, \text{mcg}\) in \(15 \, \text{ml}\). This means every \(15 \, \text{ml}\) of the solution contains \(30 \, \text{mcg}\) of the drug.

Calculating Administered Volume (ml)

To find out how many milliliters (ml) of the drug solution need to be administered, we can use the standard dosage calculation formula:

\[ \text{Volume to Administer (ml)} = \frac{\text{Desired Dose}}{\text{Available Dose}} \times \text{Volume of Available Dose} \]

Let's substitute the given values into this formula:

• Desired Dose: \(20 \, \text{mcg}\)
• Available Dose (concentration): \(30 \, \text{mcg}\)
• Volume of Available Dose: \(15 \, \text{ml}\)

Now, we can perform the calculation step-by-step:

\[ \text{Volume to Administer} = \left( \frac{20 \, \text{mcg}}{30 \, \text{mcg}} \right) \times 15 \, \text{ml} \]

First, simplify the ratio of the desired dose to the available dose:

\[ \frac{20}{30} = \frac{2}{3} \]

Now, multiply this ratio by the volume of the available dose:

\[ \text{Volume to Administer} = \frac{2}{3} \times 15 \, \text{ml} \]

\[ \text{Volume to Administer} = \frac{30}{3} \, \text{ml} \]

\[ \text{Volume to Administer} = 10 \, \text{ml} \]

Final Administered Volume

Based on the calculation, \(10 \, \text{ml}\) of the drug solution needs to be administered to provide the prescribed \(20 \, \text{mcg}\) dose.