Medication with strength 125 mg/mL has been ordered at 15 mg/kg. The patient weighs 254 lb. How much should be administered? If less than 1 round to the nearest hundredth otherwise round to the nearest tenth

First, let's break this down step by step.

### Step 1: Convert the patient's weight from pounds to kilograms.
To convert pounds (lb) to kilograms (kg), we use the conversion factor:

\[
1 \, \text{lb} = 0.453592 \, \text{kg}
\]

So the patient's weight in kilograms is:

\[
254 \, \text{lb} \times 0.453592 \, \text{kg/lb} = 115.21 \, \text{kg}
\]

### Step 2: Calculate the total amount of medication required.
The dosage is 15 mg per kg of body weight. So, the total dose in milligrams (mg) is:

\[
15 \, \text{mg/kg} \times 115.21 \, \text{kg} = 1728.15 \, \text{mg}
\]

### Step 3: Determine the volume of medication to administer.
The medication strength is 125 mg/mL, meaning each mL contains 125 mg of the drug. To find the volume needed:

\[
\text{Volume (mL)} = \frac{\text{Total dose (mg)}}{\text{Medication strength (mg/mL)}}
\]

\[
\text{Volume (mL)} = \frac{1728.15 \, \text{mg}}{125 \, \text{mg/mL}} = 13.83 \, \text{mL}
\]

### Step 4: Round the result.
Since 13.83 is greater than 1, we round to the nearest tenth:

\[
\boxed{13.8 \, \text{mL}}
\]

So, **13.8 mL** of the medication should be administered.

Would you like more details or explanations on any part of this calculation? Here are some related questions:

1. How is the conversion factor between pounds and kilograms derived?
2. Why is it important to convert the patient’s weight into kilograms before calculating the dosage?
3. What other situations might require rounding differently (e.g., to the nearest whole number)?
4. How does the medication concentration affect the volume administered?
5. What if the patient had a different weight—how would the calculations change?

**Tip:** Always double-check units when converting, especially with medication dosages!

Medication with strength 125 mg/mL has been ordered at 15 mg/kg. The patient weighs 254 lb. How much should be administered? If less than 1 round to the nearest hundredth otherwise round to the nearest tenth.

Learn how to calculate the proper dosage for a medication with 125 mg/mL concentration ordered at 15 mg/kg for a patient weighing 254 lb. This detailed step-by-step solution covers unit conversion from pounds to kilograms, dosage calculation, and volume determination. Suitable for students in Grades 9-12 and healthcare professionals.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation