Practice Problem Week 3 Weight-based practice problems 1. Vibramycin 50 mg po q 12 h is ordered for a child weighing 30 lb . The recommended dosage is 2.2 to 4.4 \( \mathrm{mg} / \mathrm{kg} / \mathrm{day} \). Is the dose safe? (prove mathematically)

To determine whether the prescribed dose of Vibramycin (doxycycline) is safe for a child weighing 30 pounds, we'll perform the following steps: 1. **Convert the Child's Weight from Pounds to Kilograms** 2. **Calculate the Total Daily Prescribed Dose** 3. **Determine the Recommended Daily Dosage Range** 4. **Compare the Prescribed Dose with the Recommended Range** Let's go through each step in detail. --- ### 1. Convert the Child's Weight from Pounds to Kilograms **Given:** - Weight = 30 pounds (lb) **Conversion Factor:** - \( 1 \text{ kg} = 2.2 \text{ lb} \) **Calculation:** \[ \text{Weight in kg} = \frac{30 \text{ lb}}{2.2 \text{ lb/kg}} \approx 13.64 \text{ kg} \] --- ### 2. Calculate the Total Daily Prescribed Dose **Given:** - Dose per administration = 50 mg - Frequency = every 12 hours (q 12 h) **Number of Doses per Day:** \[ \text{Doses per day} = \frac{24 \text{ hours}}{12 \text{ hours/dose}} = 2 \text{ doses/day} \] **Total Daily Dose:** \[ \text{Total daily dose} = 50 \text{ mg/dose} \times 2 \text{ doses/day} = 100 \text{ mg/day} \] --- ### 3. Determine the Recommended Daily Dosage Range **Given:** - Recommended dosage range = 2.2 to 4.4 mg/kg/day **Calculation:** \[ \text{Minimum recommended dose} = 2.2 \text{ mg/kg/day} \times 13.64 \text{ kg} \approx 30 \text{ mg/day} \] \[ \text{Maximum recommended dose} = 4.4 \text{ mg/kg/day} \times 13.64 \text{ kg} \approx 60 \text{ mg/day} \] **Recommended Dosage Range:** \[ 30 \text{ mg/day} \leq \text{Recommended dose} \leq 60 \text{ mg/day} \] --- ### 4. Compare the Prescribed Dose with the Recommended Range **Prescribed Total Daily Dose:** \[ 100 \text{ mg/day} \] **Recommended Daily Dose Range:** \[ 30 \text{ mg/day} \leq \text{Recommended dose} \leq 60 \text{ mg/day} \] **Analysis:** \[ 100 \text{ mg/day} > 60 \text{ mg/day (Maximum Recommended Dose)} \] --- ### **Conclusion** The prescribed total daily dose of **100 mg/day** exceeds the **maximum recommended dosage of 60 mg/day** for a child weighing 30 pounds (approximately 13.64 kg). **Therefore, the dose is **not safe** and should be re-evaluated to align with the recommended dosage guidelines.** --- **Recommendation:** Always consult with a healthcare professional before making any changes to medication dosages.