Problem 42 - Calculate With Confidence

Question

Calculate the volume necessary (in milliliters) to provide the dosage ordered, using medication labels where available. Express your answer as a decimal fraction to the nearest tenth where indicated. Order: Benadryl \(50 \mathrm{mg}\) p.o. at bedtime. Available: Benadryl elixir \(12.5 \mathrm{mg}\) per \(5 \mathrm{~mL}\) _______.

Step-by-Step Solution

Answer

The volume needed is 20.0 mL.

Step 1: Understand the Order

The order requires administering 50 mg of Benadryl at bedtime. We need to determine how many milliliters of the available elixir provide this dosage.

Step 2: Analyze the Available Solution

The medication available is Benadryl elixir with a concentration of 12.5 mg per 5 mL.

Step 3: Set Up the Proportion

Since we know the concentration of the elixir, we can set up a proportion to find the volume that contains 50 mg of the medication: \(\frac{12.5 \, \mathrm{mg}}{5 \, \mathrm{mL}} = \frac{50 \, \mathrm{mg}}{x \, \mathrm{mL}}\).

Step 4: Solve the Proportion

Cross-multiply to solve for \(x\):\[12.5 \, \mathrm{mg} \times x \, \mathrm{mL} = 50 \, \mathrm{mg} \times 5 \, \mathrm{mL}\] \[12.5x = 250\] \[x = \frac{250}{12.5} = 20\].

Step 5: Express the Answer Important to the Question

The required volume is 20 mL, expressed as a decimal fraction to the nearest tenth.

Key Concepts

Medication Concentration

Medication concentration is a crucial element in dosage calculation. It refers to the amount of active ingredient, in this case, Benadryl, present in a given volume of the solution.
For the Benadryl elixir available, the concentration provided is 12.5 mg per 5 mL. This means every 5 milliliters of this liquid contains 12.5 milligrams of Benadryl, the active ingredient that produces the therapeutic effect.

• This concentration is crucial for accurately providing the right dosage.
• Helps ensure that the patient receives the intended amount of medication for therapeutic effectiveness.

When dealing with medication, always note this concentration as it helps you understand how much of the medicine you are actually administering.

Proportions in Math

A basic mathematics concept used in calculating medication dosages is proportions. A proportion is an equation that states two ratios are equivalent.
In the context of this exercise, to find how much Benadryl elixir is needed for a prescribed dosage, setting up a proportion is key.
Given the problem:

• The known concentration is a ratio: 12.5 mg per 5 mL.
• The ordered dose is 50 mg.

Hence, the proportion is set as: \(\frac{12.5 \, \mathrm{mg}}{5 \, \mathrm{mL}} = \frac{50 \, \mathrm{mg}}{x \, \mathrm{mL}}\).
This proportion helps in understanding that \(x\), the unknown volume of mL required, should correspond to the 50 mg dosage ordered.
Using cross-multiplication, the equation allows you to find \(x\), ensuring that your dosage calculation is accurate and efficient.

Volume Measurement

Volume measurement is about determining the amount of space that a substance takes up. In medication dosage calculation, it means determining how many milliliters (mL) are required to meet a specific dosage.
Understanding volume measurement in the context of medication involves:

• Identifying the required dosage in milligrams (mg).
• Calculating how many milliliters (mL) are necessary using the concentration ratio given.

In our scenario, after calculating, we find that 20 mL of the Benadryl elixir provides precisely 50 mg of the medication required. This reflects the calculated proportion that matches the ordered dosage.
Accuracy in volume measurement is vital, as administering the incorrect volume could lead to underdosing or overdosing, thus impacting patient safety.