Problem 8 - Calculate With Confidence

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. Keflex (cephalexin) suspension \(250 \mathrm{mg}\) p.o. qoh is ordered for a child weighing \(66 \mathrm{lb}\). The usual pediatric dosage is 25 to \(50 \mathrm{mg} / \mathrm{kg} /\) day in four divided dosages. Available: Keflex suspension \(250 \mathrm{mg}\) per \(5 \mathrm{~mL}\) a. Is the dosage ordered safe? (Prove mathematically.) b. How many milliliters would you need to administer one dosage? Calculate the dose if the order is safe.

Step-by-Step Solution

Answer

The dosage is safe. Administer 5 mL per dose.

Step 1: Convert Weight to Kilograms

To find the appropriate dosage range, we need the weight in kilograms. Since 1 kg = 2.2 lbs, we convert the child's weight from pounds to kilograms: \( 66 \text{ lbs} \div 2.2 \text{ lbs/kg} = 30 \text{ kg} \). So, the child weighs 30 kg.

Step 2: Calculate Dosage Range

The usual pediatric dosage is between 25 to 50 mg/kg/day. Therefore: \( 25 \text{ mg/kg/day} \times 30 \text{ kg} = 750 \text{ mg/day} \) and \( 50 \text{ mg/kg/day} \times 30 \text{ kg} = 1500 \text{ mg/day} \). The safe dosage range is 750 mg/day to 1500 mg/day.

Step 3: Check Ordered Dosage Safety

The ordered dosage is 250 mg every 6 hours (qoh means every 6 hours). Thus, the total daily dosage is \( 250 \text{ mg} \times 4 = 1000 \text{ mg/day} \). This falls within the safe range of 750 mg/day to 1500 mg/day. Therefore, the dosage is safe.

Step 4: Calculate Milliliters Per Dose

Keflex suspension is available as 250 mg per 5 mL. To find the volume needed for one dose, we set up a proportion: \( \frac{250 \text{ mg}}{5 \text{ mL}} = \frac{250 \text{ mg}}{x \text{ mL}} \). Solving for \( x \), we find \( x = 5 \text{ mL} \). Thus, one 250 mg dose requires 5 mL of the suspension.

Key Concepts

Body Weight Conversion

When it comes to pediatric dosage calculations, converting the body weight from pounds to kilograms is crucial. Medication dosages for children are often based on their body weight in kilograms because it provides a more precise measurement that accounts for their smaller size compared to adults.

The conversion is simple: Divide the weight in pounds by 2.2 to get the weight in kilograms. For our specific exercise, the child weighs 66 pounds.

We perform the calculation: \[66 \text{ lbs} \div 2.2 \text{ lbs/kg} = 30 \text{ kg}\] This means the child weighs 30 kilograms. Knowing this weight accurately is key to determining the correct and safe dosage range for any medication.

Safe Dosage Range

Understanding the safe dosage range is essential in pediatric care to avoid overmedication or underdosing. For the drug Keflex, the usual pediatric dosage is between 25 and 50 mg per kilogram per day.

To calculate the safe range for our child, who is 30 kg, we perform the following calculations:Lower range:\[25 \text{ mg/kg/day} \times 30 \text{ kg} = 750 \text{ mg/day}\] Upper range:\[50 \text{ mg/kg/day} \times 30 \text{ kg} = 1500 \text{ mg/day}\] Thus, the safe daily dosage range for the child is between 750 mg and 1500 mg. The dosage ordered, which totals 1000 mg per day, comfortably falls within this range, making it safe for the child to take this medication.

Milliliters Per Dose

Determining how many milliliters to administer per dose is straightforward once the correct dosage is known. The prescribed medication, Keflex, comes in a concentration of 250 mg per 5 mL.

Since the ordered dose is 250 mg every 6 hours, we calculate the volume using the given concentration:\[\frac{250 \text{ mg}}{5 \text{ mL}} = \frac{250 \text{ mg}}{x \text{ mL}}\] With this proportion, solving for \(x\) gives us:\[x = 5 \text{ mL}\] This means for each dose, we need to administer 5 mL of the Keflex suspension to deliver the correct amount of medication. This step ensures that the child's dosage aligns with the prescribed guidelines.

Mathematical Proof of Dosage

Verifying the safety of the ordered dosage via a mathematical approach is a reassuring step. For Keflex, the order is 250 mg every 6 hours, totaling four doses per day.

Let's calculate:Daily dosage: \[250 \text{ mg/dose} \times 4 \text{ doses per day} = 1000 \text{ mg/day}\] This total dosage sits within the safe range of 750 mg to 1500 mg per day calculated earlier, confirming its safety.

By evaluating both the calculated daily total and comparing it to the safe range, we ensure that the administered dosage is not only effective but also safe, cementing the importance of this mathematical assessment in pediatric medication.