Question

Calculate the dosages to be given. Round answers to the nearest tenth as indicated (express answers in milliliters). Order: Ferrous sulfate \(45 \mathrm{mg}\) p.o. every day. Available: Ferrous sulfate drops \(15 \mathrm{mg}\) per \(0.6 \mathrm{~mL}\)

Short answer

1.8 mL

Step-by-step solution

Understand the Order

The order requires the patient to receive 45 mg of ferrous sulfate orally each day. This is the target dosage we need to achieve with the available supply.

Analyze the Available Supply

The available supply is ferrous sulfate drops that provide 15 mg of ferrous sulfate per 0.6 mL. We need to figure out how much solution provides the 45 mg needed as per the order.

Calculate the Dosage Needed

Using the concentration of the available supply, calculate how many milliliters of solution are needed to provide the required 45 mg. We use the ratio given: 15 mg in 0.6 mL.

Set Up the Proportion

Set up the proportion based on the available concentration to find the unknown volume. Let \( x \) be the volume we need, solving:\[\frac{15}{0.6} = \frac{45}{x}\]

Solve for x

Cross-multiply and solve for \( x \):\[15 \cdot x = 45 \cdot 0.6\]This simplifies to:\[15x = 27\]Divide both sides by 15:\[x = \frac{27}{15} = 1.8 \text{ mL}\]

Round the Result

The result, 1.8 mL, is already rounded to the nearest tenth, as required.

Key concepts

Pharmacology

Pharmacology is the branch of medicine focused on the uses, effects, and modes of action of drugs. Understanding pharmacology is crucial for healthcare practitioners as it involves knowing how different drugs interact within the body. When calculating dosages, as we did in the given exercise, it's vital to understand both the desired therapeutic effect and the correct amount needed to achieve this effect. In this case study, we are dealing with ferrous sulfate, which is often prescribed to treat iron deficiency anemia. Knowing the specific drug and its form—here, a drop formulation—helps in determining the correct dosage. Each drug can have different concentrations and formulations, which influences how it should be administered. Healthcare professionals should also be aware of how medications like ferrous sulfate are absorbed, metabolized, and excreted by the body. This knowledge helps in tailoring the dosage to the individual patients' needs, optimizing the therapeutic benefits while minimizing potential side effects.

Mathematics in Healthcare

Mathematics in healthcare is essential for calculating the correct dosages, understanding patient metrics, and ensuring precise medication distribution. Calculating drug dosages accurately is a skill every healthcare professional must master, to ensure patient safety and therapeutic efficacy. In the exercise, we calculated how many milliliters of a drug formulation are needed. This involves understanding ratios—a critical mathematical concept in healthcare. We were given that 15 mg of medication corresponds to 0.6 mL. In order to calculate the volume needed for 45 mg, we set up a proportion equation: - 15 mg : 0.6 mL = 45 mg : x mL Solving for \( x \) by cross-multiplication allows us to find the correct volume of medication needed: - \( 15 \cdot x = 45 \cdot 0.6 \) which simplifies to \( x = 1.8 \) mL. It’s crucial to understand the step-by-step methodology in such calculations, as dosage errors can lead to inadequate treatment or adverse side effects.

Nursing Education

Nursing education prepares future nurses to undertake various essential tasks, including medicine administration, patient care, and clinical decision-making. A vital part of this education is learning to calculate medication dosages accurately. This exercise is a common question type that nursing students encounter as part of their training. Students are trained to understand doctor's orders accurately, analyze available medications, and execute the necessary calculations to provide the right amount of a drug to a patient. The step-by-step solution provided ensures that nurses develop a solid foundation in medication administration. More importantly, nursing education emphasizes the application of theory to practice, which includes understanding why specific calculations are required, ensuring precision, and the importance of rounding correctly, as in rounding 1.8 to the nearest tenth in this example. These skills help prevent errors in real-world patient care and are a critical component of nursing responsibilities.