Question

Calculate the dosages to be given. Round answers to the nearest tenth as indicated (express answers in milliliters). Order: Theophylline \(40 \mathrm{mg}\) p.o. q.i.d. Available: Theophylline elixir labeled \(80 \mathrm{mg}\) per \(15 \mathrm{~mL}\)

Short answer

7.5 mL per dose, four times a day.

Step-by-step solution

Understand the Prescription

The doctor has prescribed Theophylline at a dose of 40 mg, to be taken orally four times a day (q.i.d. means "four times a day").

Determine the Concentration of Available Elixir

The available Theophylline elixir has a concentration of 80 mg of the drug per 15 mL of solution. This means that each 15 mL of the elixir contains 80 mg of Theophylline.

Set Up a Proportion to Find Required Volume

To determine how many milliliters will contain the ordered 40 mg of Theophylline, set up a proportion using the known concentration:\[ \frac{80 \text{ mg}}{15 \text{ mL}} = \frac{40 \text{ mg}}{x \text{ mL}} \]Where \(x\) is the volume of elixir that contains 40 mg.

Solve the Proportion

Cross multiply to solve for \(x\):\[ 80 \times x = 40 \times 15 \]This simplifies to:\[ 80x = 600 \]Divide both sides by 80:\[ x = \frac{600}{80} = 7.5 \text{ mL} \]

Conclude the Required Dosage

The required volume of Theophylline elixir for one dose is 7.5 mL. Therefore, the patient should take 7.5 mL of the elixir four times a day.

Key concepts

Medication Administration

Proper medication administration is crucial for ensuring patient safety and effective treatment. It involves knowing and understanding the prescribed medicine, how it should be given, and ensuring the correct dosage is administered as specified by the healthcare provider. In the exercise provided, Theophylline is the prescribed medication at a dosage of 40 mg to be taken by mouth (p.o.), four times daily (q.i.d.).

Understanding medication instructions includes recognizing abbreviations such as q.i.d., which informs you the dosage is required four times a day. Each administration must follow the prescribed routine to avoid underdosing or overdosing, which can have significant health implications.

• **Check prescription details:** Ensure you understand the dosage, frequency, and method of administration (e.g., oral, topical).
• **Set reminders:** If a medication needs to be taken multiple times daily, use alarms or reminders to maintain consistent administration times.
• **Document doses:** Keep a log of each dose taken to avoid missed or repeated doses.

Each of these steps ensures that you adhere to the prescribed regimen safely and effectively, contributing to optimal patient care outcomes.

Pharmaceutical Calculations

Pharmaceutical calculations are essential skills for determining the correct dosage, especially when the available concentration differs from the required amount. The problem here requires you to calculate the correct volume of the Theophylline elixir needed to meet the prescribed 40 mg dose when the available concentration is 80 mg per 15 mL.

To perform these calculations, one needs to understand how to manipulate and rearrange concentration and volume data. This ensures that the administered medication is both safe and effective for the patient. Consider the following points:

• **Understand concentrations:** Concentration tells you how much drug is in a given amount of solution. In this example, 80 mg of Theophylline is in every 15 mL.
• **Use unit conversion and arithmetic operations:** Be comfortable converting and manipulating units to ensure the figures align for multiplication or division.
• **Check calculations carefully:** Before administering medication, double-check calculations to confirm the correct dose and ensure patient safety.

Proper pharmaceutical calculations ensure the right amount of medication is given, minimizing the risk of errors.

Proportion Method

The proportion method is a straightforward mathematical technique used to calculate unknown values. It is particularly handy in pharmaceutical calculations, where dosages often need to be adapted to different concentrations. The core idea is to maintain the same ratio between different sets of values.

In the given exercise, the goal is to find the volume of elixir that contains the prescribed dose of 40 mg. You are given a known concentration of 80 mg per 15 mL. By setting up a proportion, you equate two ratios: the known concentration and the desired dosage. Here’s how it works:

• **Identify known ratios:** Use the concentration information provided (e.g., 80 mg per 15 mL).
• **Set up a proportion:** Equate the known ratio with the unknown quantity (e.g., \( \frac{80 \text{ mg}}{15 \text{ mL}} = \frac{40 \text{ mg}}{x \text{ mL}} \)).
• **Solve for the unknown:** Cross multiply and divide accordingly to solve for the unknown amount (\( x \)).

This method simplifies the task of finding missing values and is a reliable tool for ensuring accuracy in pharmaceutical practices.