Question

Read the dosage information or label given for the following problems. Express body weight conversion to the nearest tenth where indicated and dosages to the nearest tenth. The recommended dosage for Mithracin for the treatment of testicular tumors is 25 to \(30 \mathrm{mcg} / \mathrm{kg} .\) A client weighs \(190 \mathrm{lb}\). a. What is the client's weight in kilograms to the nearest tenth? b. What is the dosage range in milligrams for this client? (Round to the nearest tenth.)

Short answer

a. 86.2 kg b. 2.2 to 2.6 mg

Step-by-step solution

Convert Pounds to Kilograms

First, we need to convert the client's weight from pounds to kilograms. The conversion factor is \(1 \text{ lb} = 0.453592 \text{ kg}\).\[ \text{Weight in kg} = 190 \text{ lb} \times 0.453592 \frac{\text{kg}}{\text{lb}} = 86.18348 \text{ kg} \]Round this to the nearest tenth gives 86.2 kg.

Calculate the Minimum Dosage

Use the minimum recommended dosage of Mithracin, which is 25 mcg/kg.\[ \text{Minimum dosage} = 25 \frac{\text{mcg}}{\text{kg}} \times 86.2 \text{ kg} = 2155 \text{ mcg} \]Convert to milligrams using \(1 \text{ mg} = 1000 \text{ mcg}\).\[ 2155 \text{ mcg} = 2.155 \text{ mg} \]Round to the nearest tenth gives 2.2 mg.

Calculate the Maximum Dosage

Use the maximum recommended dosage of Mithracin, which is 30 mcg/kg.\[ \text{Maximum dosage} = 30 \frac{\text{mcg}}{\text{kg}} \times 86.2 \text{ kg} = 2586 \text{ mcg} \]Convert to milligrams.\[ 2586 \text{ mcg} = 2.586 \text{ mg} \]Round to the nearest tenth gives 2.6 mg.

Key concepts

Body Weight Conversion

When calculating medication dosages, knowing the patient’s body weight in the correct unit is crucial. This often involves converting pounds to kilograms, especially in medical scenarios where precise medication dosing is key. The conversion factor we use is

• 1 pound (lb) = 0.453592 kilograms (kg)

To convert, multiply the number of pounds by 0.453592. For example, if a client weighs 190 lbs, their weight in kilograms is calculated as:\[ 190 ext{ lb} imes 0.453592 rac{ ext{kg}}{ ext{lb}} = 86.18348 ext{ kg} \]Then, rounding 86.18348 to the nearest tenth gives you 86.2 kg. This conversion process is essential because dosing often depends on body weight in kilograms.

Kilogram Conversion

Converting weight into kilograms from pounds isn’t just about applying a simple multiplication. Attention to precision and rounding is also important to ensure accuracy in the dosage calculations.

• It's crucial to always round to the nearest tenth when required.
• In our example, converting 190 pounds yields 86.18348 kg. Rounding it to the nearest tenth gives us 86.2 kg.

The conversion and rounding must be accurate because small errors can lead to incorrect dosages, which might be either too much or too little of the medication. Always double-check your math to ensure patient safety and accurate dosing.

Medication Dosage Range

Determining the correct dosage range of medication for a patient based on body weight is slightly more involved than simple arithmetic. Here's a quick breakdown:

• First, identify the recommended dosage range per kilogram of body weight. For Mithracin, it's 25-30 mcg/kg.
• Then, multiply the entire range by the patient’s weight in kilograms to find their specific dosage range.

Using the minimum dose of 25 mcg/kg, multiplied by 86.2 kg, results in:\[ 25 rac{mcg}{kg} \times 86.2 ext{ kg} = 2155 ext{ mcg} \]Convert to milligrams by dividing by 1000 and rounding to the nearest tenth results in 2.2 mg. For the maximum dose of 30 mcg/kg:\[ 30 rac{mcg}{kg} \times 86.2 ext{ kg} = 2586 ext{ mcg} \]Converting and rounding this provides 2.6 mg. Thus, the correct dosage range for our client is 2.2 mg to 2.6 mg. Proper calculations are vital for giving the patient the most effective and safe dosage possible.