Problem 33 - Prealgebra

Question

Nursing For children, the amount of medicine prescribed is often determined by the child's mass. Usually it is calculated from the milligrams per kilogram per day listed on the medication's box. How much should an 18 kg child be given a day if the dosage is 50 mg/kg/day?

Step-by-Step Solution

Answer

An 18 kg child should be given 900 mg of medicine per day.

Step 1: Understand the Problem

We need to determine the total daily dosage of medicine for a child who weighs 18 kg, given that the medicine is prescribed at a dosage of 50 mg/kg/day.

Step 2: Formula for Dosage Calculation

The dosage is calculated using the formula: \[ \text{Total Dosage} = \text{Dosage per kilogram} \times \text{Child's Mass (kg)} \] where "Dosage per kilogram" is given as 50 mg/kg, and the "Child's Mass" is 18 kg.

Step 3: Solve for Total Dosage

Substitute the values into the formula: \[ \text{Total Dosage} = 50 \text{ mg/kg} \times 18 \text{ kg} \] Calculate the product to find the total dosage in mg.

Step 4: Calculate the Product

Perform the calculation: \[ 50 \text{ mg/kg} \times 18 \text{ kg} = 900 \text{ mg} \] Thus, the total daily dosage of medicine for the child is 900 mg.

Key Concepts

Child Mass in Dosage Calculation

When determining the correct amount of medication for a child, knowing the child's mass (or weight) is crucial. Medication dosages often rely on body weight to ensure the child receives a safe, yet effective amount. Calculating based on mass helps in customizing the medicine for each child's unique characteristics.

Here’s why mass is so important:

• Every kilogram of body weight requires a specific amount of medication to achieve the desired effect.
• This method minimizes the risk of underdosing or overdosing.
• Children have varying growth rates, and their weights change. Tailoring the dosage ensures their medical needs are met accurately.

In our example, the child's mass is 18 kg. This piece of information will be used to accurately calculate the proper daily dosage of medicine.

Total Dosage Formula

The total dosage formula is a key step in calculating how much medication a child needs. To compute the daily dosage, you simply multiply the dosage per kilogram by the child’s weight in kilograms. This formula is straightforward and can be applied to various prescriptions.

For our problem, the formula is:\[\text{Total Dosage} = \text{Dosage per kilogram} \times \text{Child's Mass (kg)}\]The dosage per kilogram is a standard number provided on medicine packaging, in this case, 50 mg/kg. The child's mass is 18 kg, a constant we obtain from their weight.

Applying the formula ensures that each calculation adapts to the child's specific requirements, leading to a precise and effective dosage.

Dosage Calculation Steps

Knowing how to calculate the correct dosage involves a few clear steps. Breaking it down makes it easier to understand:

• Understand the Problem: Identify key data, like the child's weight and the dosage per kilogram.
• Substitute into Formula: Use the formula \( \text{Total Dosage} = 50 \text{ mg/kg} \times 18 \text{ kg} \).
• Calculate the Total Dosage: Multiply the given values to find the total daily dosage.
• Verify the Result: Always double-check that the calculated dosage aligns with the typical range for that medication.

In our example, multiplying 50 by 18 gives us 900 mg. This is the amount the child should receive per day. Following these steps ensures accuracy and safety in medication administration.