Problem 49 - Calculate With Confidence

Question

Calculate the following dosages using the medication label or information provided. Label answers correctly: tabs, caps, mL. Answers expressed in milliliters should be rounded to the nearest tenth where indicated. Order: Benadryl 30 mg p.o. t.i.d. Available: Oral solution labeled 12.5 mg per 5 mL _____________________________

Step-by-Step Solution

Answer

12.0 mL per dose

Step 1: Understanding the Order

The order requires the patient to receive 30 mg of Benadryl per dose. The term "p.o." means by mouth, and "t.i.d." means three times a day. Our goal is to determine how many milliliters (mL) of the oral solution is needed to provide 30 mg per dose.

Step 2: Understanding the Medication Available

The medication is available as an oral solution with a concentration of 12.5 mg of Benadryl per 5 mL. We need to use this information to calculate the required volume for a 30 mg dose.

Step 3: Set Up the Proportion

Set up the proportion to solve for the unknown volume (x mL):\[\frac{12.5 \, \text{mg}}{5 \, \text{mL}} = \frac{30 \, \text{mg}}{x \, \text{mL}}\]

Step 4: Solve for x

Cross-multiply to solve for \(x\):\[12.5x = 30 \times 5\]\[12.5x = 150\]Divide both sides by 12.5:\[x = \frac{150}{12.5}\]\[x = 12\]

Step 5: Round to the Nearest Tenth

Since the answer needs to be rounded to the nearest tenth, and 12 is already a whole number ending in a zero, it can be expressed as 12.0 mL.

Step 6: Final Answer

The final step is to provide the answer based on calculations. For each dose, the patient needs 12.0 mL of the oral solution.

Key Concepts

Medication Dosage

When it comes to administering medications, understanding the correct dosage is crucial. Medication dosage refers to the precise amount of medicine a patient needs to receive to achieve the desired therapeutic effect. It's like solving a puzzle where each piece, or dosage, should fit perfectly to ensure the patient's safety and the medicine's effectiveness.
To determine the correct dosage, health professionals need a comprehensive understanding of the doctor's order, such as the specific drug, the amount prescribed, and the method of administration. In this exercise, the doctor ordered 30 mg of Benadryl to be taken orally three times a day. Understanding the order is the first essential step towards calculating the accurate dosage the patient requires.

Proportion Method

The proportion method is a powerful technique used in dosage calculations. It involves setting up a mathematical equation or ratio to determine an unknown quantity. This method is particularly handy when dealing with medication concentrations and allows us to solve for the required dosage in a straightforward manner.
In the given exercise, the proportion method helped in determining how much of the oral solution delivers the 30 mg dose. We set up a proportion based on the available information: 12.5 mg of Benadryl per 5 mL of solution. The goal was to find the equivalent volume (x) that provides 30 mg:

• Known: 12.5 mg = 5 mL
• Unknown: 30 mg = x mL

By solving the proportion \( \frac{12.5 \, \text{mg}}{5 \, \text{mL}} = \frac{30 \, \text{mg}}{x \, \text{mL}} \), we found that x equals 12 mL.

Oral Solutions

Oral solutions are liquid medicines that are swallowed by mouth. They offer a convenient way for patients, especially those who have difficulty taking tablets or capsules, to receive medication. Often, oral solutions are measured in milliliters (mL) and provide a specific amount of the active ingredient per unit volume of the liquid.
The Benadryl in this exercise was available as an oral solution with a concentration of 12.5 mg per 5 mL. This information was pivotal for calculating the correct amount of solution needed for each 30 mg dose. Ensuring the proper measurement is made with a specialized medicine cup or syringe to provide the patient with an accurate dose is also essential.

Rounding Techniques

Rounding techniques are important in medication dosage calculations to ensure the prescribed dosage is not only precise but also safe and practical for administration. This becomes essential when working with decimals, as small errors can lead to incorrect dosages.
In this exercise, we needed to round the calculated volume of oral solution to the nearest tenth. Since the exact answer turned out to be 12 mL, the rounding was straightforward — no actual change was needed — but if we were working with a decimal result, rounding would adjust it to the nearest tenth of a milliliter. This helps in making sure the dosage aligns with the measurement tools typically used in medication administration.