Question

A client began receiving \(325 \mathrm{mg}\) (milligrams) of a medication. The prescriber increased the dosage of medication by \(10 \% .\) What will the new dosage be? ______\(\mathrm{mg}\)

Short answer

The new dosage is 357.5 mg.

Step-by-step solution

Understand the Problem

The client initially receives a dosage of 325 mg. The dosage is being increased by 10%. We need to calculate the new dosage after this increase.

Calculate the Increase

To find the amount of increase, we need to calculate 10% of 325 mg. This is done by multiplying 325 mg by 0.10 (which is the decimal representation of 10%). Let's calculate:\[ 0.10 \times 325 = 32.5 \]So, the increase in dosage is 32.5 mg.

Add the Increase to the Original Dosage

To find the new dosage, add the increase we calculated in Step 2 to the original dosage. The original dosage is 325 mg and the increase is 32.5 mg:\[ 325 + 32.5 = 357.5 \]Therefore, the new dosage is 357.5 mg.

Key concepts

Medication Dosage

Medication dosage refers to the specific amount of a medication prescribed to be taken at a particular time. It is crucial to administer the correct dosage as per the prescription to ensure both efficacy and safety.
For accuracy, dosages are often measured in milligrams (mg), micrograms (mcg), or sometimes in milliliters (ml) if the medication is in liquid form.
The prescribed dosage can vary based on several factors:

• The patient's age and weight
• The severity of the condition being treated
• The patient's response to previous doses
• And, specific guidance from the prescriber

Even a small error in medication dosage can lead to ineffective treatment or potential harm, thus precision in dosage calculation is critical for medical practitioners.

Percentage Increase

When understanding how much a certain value has increased, we often use percentage increase to express this change. In the context of medication, a percentage increase shows the additional amount of drug administered compared to the original dose.
To calculate the percentage increase, you follow a simple mathematical process:

• Convert the percentage into a decimal by dividing by 100. E.g., 10% becomes 0.10.
• Multiply this decimal by the original dosage.
• The result indicates how much the dosage will increase.

For example, in the given exercise, a 10% increase of a 325 mg dose results in an increase of 32.5 mg. Understanding this concept helps ensure medications are adjusted correctly for optimal therapeutic results.

Mathematical Problem Solving

Mathematical problem solving is an essential skill, not just in academic contexts but also in real-world applications like healthcare. Like the given exercise, it often involves several logical steps:
Firstly, understanding the problem is critical. In this case, knowing that the initial dosage is 325 mg and is to be increased by 10% is essential.
Next, calculate the change using appropriate mathematical operations, such as multiplication, to determine the increase as a percentage of the original.
Finally, accurately combining this new information with the original data results in the correct solution.
These skills not only help solve medication-related queries but also foster critical thinking and problem-solving capabilities useful across various disciplines.

Nursing Calculations

Nurses frequently perform dosage calculations as part of their daily responsibilities. These calculations can include percentage increases, dosage conversions, and understanding complex medication orders.
Accurate nursing calculations ensure the following:

• The patient receives the correct medication amount.
• The risk of underdosing or overdosing is minimized.
• The effectiveness of the prescribed treatment is maximized.

Mastering this aspect of nursing involves not just understanding mathematical principles but also knowing how to apply them in clinical settings.
Educational platforms and training often emphasize practical examples and exercises to enhance these essential skills, ensuring that nurses are well-equipped to handle a variety of dosage scenarios in patient care.