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 \(30 \mathrm{mg}\) p.o. t.i.d. Available: Oral solution labeled \(12.5 \mathrm{mg}\) per \(5 \mathrm{~mL}\) ______

Step-by-Step Solution

Answer

12 mL

Step 1: Understand the Order

The order requires a dosage of Benadryl of 30 mg by mouth (p.o.), three times a day (t.i.d.). This means the patient needs to take a 30 mg dose each time.

Step 2: Analyze the Medication Available

The medication available is an oral solution with a concentration of 12.5 mg per 5 mL. This means in every 5 mL of the solution, there is 12.5 mg of Benadryl.

Step 3: Set Up a Proportion to Find the Volume Required

To find out how many mL of the solution is needed for 30 mg of Benadryl, set up the following proportion:\[\frac{12.5 \, \text{mg}}{5 \, \text{mL}} = \frac{30 \, \text{mg}}{x \, \text{mL}}\]Here, \(x\) represents the volume in mL needed to administer a 30 mg dose.

Step 4: Solve the Proportion

Cross-multiply to solve the proportion:\[12.5x = 30 \times 5\]\[12.5x = 150\]Next, divide both sides by 12.5 to isolate \(x\):\[x = \frac{150}{12.5}\]\[x = 12\]

Step 5: Round and Label the Answer

The calculation resulted in 12 mL of the oral solution needed for each 30 mg dose. Since the solution measures are already in whole mL, no further rounding is needed. The final answer is labeled as 12 mL.

Key Concepts

Understanding the Proportion Method

The proportion method is a valuable tool for calculating medication dosages, especially when dealing with different medication formulations. It relies on the concept of equivalent ratios. By setting up a proportion, you can determine one unknown quantity based on a known quantity.
Let's break this down with our example. You have an available oral solution with a concentration of 12.5 mg per 5 mL. The doctor's order is for 30 mg of Benadryl. To calculate the required milliliters for the 30 mg dose, you set up a proportion:

• Left side: The known dosage, 12.5 mg in 5 mL.
• Right side: The desired dosage, 30 mg in an unknown volume ( mL).

The proportion is written as:\[ \frac{12.5 \text{ mg}}{5 \text{ mL}} = \frac{30 \text{ mg}}{x \text{ mL}} \]From here, cross-multiply to solve for the unknown volume \(x\). This gives you the equation:\[12.5x = 150\]By dividing both sides by 12.5, you find \(x\) equals 12 mL. The method ensures that the ratio of the medication's strength is maintained in the required dosage.

What is an Oral Solution?

An oral solution is a liquid medication designed for oral consumption. It involves dissolving a drug in a solvent, usually water, to form a uniform mixture. This form of medication is particularly suitable for patients who may have difficulty swallowing pills, such as children or the elderly.

Oral solutions offer several advantages:

• They provide an easy way to adjust doses precisely according to a patient's needs.
• The liquid form allows for quicker absorption in the body compared to solid forms like pills or capsules.
• It's often preferred for medications that are required in exact doses, making it easier to calculate and administer the accurate amount prescribed.

In our exercise, the oral solution of Benadryl measured at 12.5 mg per 5 mL allows healthcare providers to efficiently adjust dosages to meet the patient's required 30 mg dosage by using the calculated 12 mL for each administration.

Accurate Milliliter Measurement

Measuring liquid medications accurately is crucial. The unit of milliliter (mL) is typically used when dealing with oral solutions. This measurement ensures that a patient receives the correct dose of medication. Even slight inaccuracies can lead to underdosing or overdosing, both of which can have serious implications for patient health.

Follow these tips for accurate measurement:

• Always use medical-grade syringes or measuring cups with clear, calibrated markings.
• Check the measurement at eye level to ensure precision.
• Avoid using household utensils like teaspoons, as they can vary greatly in volume and are not reliable.

In the given exercise, we calculated that each dose of Benadryl should be 12 mL. Ensuring that this volume is measured accurately at each administration is crucial for patient safety and medication efficacy.