NR322 Peds Math Practice Problems

12 August 2024

Theophylline (Theostat)

  • Order: 65 mg per NG QID (4 times a day) for a 3 y/o child weighing 9.9 kg.
  • Safe dose: 22 mg/kg/day Q 6 hours.
  • Stock concentration: 80 mg/15 ml.

Step 1: Calculate the safe dose per day.Safe dose per day=22 mg/kg/day×9.9 kg=217.8 mg/day\text{Safe dose per day} = 22 \text{ mg/kg/day} \times 9.9 \text{ kg} = 217.8 \text{ mg/day}Safe dose per day=22 mg/kg/day×9.9 kg=217.8 mg/day

Step 2: Calculate the safe dose per administration (since QID = 4 doses per day).Safe dose per administration=217.8 mg/day4=54.45 mg\text{Safe dose per administration} = \frac{217.8 \text{ mg/day}}{4} = 54.45 \text{ mg}Safe dose per administration=4217.8 mg/day​=54.45 mg

Step 3: Compare the ordered dose to the safe dose.The ordered dose is 65 mg, which is higher than the safe dose of 54.45 mg. Therefore, the ordered dose is not safe.

Step 4: Calculate the amount needed based on the ordered dose.Volume required=65 mg80 mg/15 ml×15 ml=12.19 ml\text{Volume required} = \frac{65 \text{ mg}}{80 \text{ mg/15 ml}} \times 15 \text{ ml} = 12.19 \text{ ml}Volume required=80 mg/15 ml65 mg​×15 ml=12.19 ml

2. Ceftazidime (Tazicef or Fortaz)

  • Order: 280 mg IV q8h in 10 ml D5/1/3 NS for a 4 y/o child weighing 17 kg.
  • Safe dose: 1 mo-12 y/o: 30-50 mg/kg/day Q 8 hours; not to exceed 6 Gm/day.
  • Stock concentration after reconstitution: 95 mg/ml.

Step 1: Calculate the safe dose range per day.Safe dose (lower range)=30 mg/kg/day×17 kg=510 mg/day\text{Safe dose (lower range)} = 30 \text{ mg/kg/day} \times 17 \text{ kg} = 510 \text{ mg/day}Safe dose (lower range)=30 mg/kg/day×17 kg=510 mg/daySafe dose (upper range)=50 mg/kg/day×17 kg=850 mg/day\text{Safe dose (upper range)} = 50 \text{ mg/kg/day} \times 17 \text{ kg} = 850 \text{ mg/day}Safe dose (upper range)=50 mg/kg/day×17 kg=850 mg/day

Step 2: Calculate the safe dose per administration (since q8h = 3 doses per day).Safe dose per administration (lower range)=510 mg/day3=170 mg\text{Safe dose per administration (lower range)} = \frac{510 \text{ mg/day}}{3} = 170 \text{ mg}Safe dose per administration (lower range)=3510 mg/day​=170 mgSafe dose per administration (upper range)=850 mg/day3=283.33 mg\text{Safe dose per administration (upper range)} = \frac{850 \text{ mg/day}}{3} = 283.33 \text{ mg}Safe dose per administration (upper range)=3850 mg/day​=283.33 mg

Step 3: Compare the ordered dose to the safe dose range.The ordered dose is 280 mg, which falls within the safe dose range (170 mg to 283.33 mg). The ordered dose is safe.

Step 4: Calculate the amount needed based on the ordered dose.Volume required=280 mg95 mg/ml=2.95 ml\text{Volume required} = \frac{280 \text{ mg}}{95 \text{ mg/ml}} = 2.95 \text{ ml}Volume required=95 mg/ml280 mg​=2.95 ml

3. Meperidine HCL (Demerol)

  • Order: 20 mg IM stat pre-op for a child weighing 35 pounds.
  • Safe dose: 1-2 mg/kg.
  • Stock concentration: 50 mg/ml.

Step 1: Convert the child’s weight from pounds to kilograms.35 pounds÷2.2=15.91 kg35 \text{ pounds} \div 2.2 = 15.91 \text{ kg}35 pounds÷2.2=15.91 kg

Step 2: Calculate the safe dose range.Safe dose (lower range)=1 mg/kg×15.91 kg=15.91 mg\text{Safe dose (lower range)} = 1 \text{ mg/kg} \times 15.91 \text{ kg} = 15.91 \text{ mg}Safe dose (lower range)=1 mg/kg×15.91 kg=15.91 mgSafe dose (upper range)=2 mg/kg×15.91 kg=31.82 mg\text{Safe dose (upper range)} = 2 \text{ mg/kg} \times 15.91 \text{ kg} = 31.82 \text{ mg}Safe dose (upper range)=2 mg/kg×15.91 kg=31.82 mg

Step 3: Compare the ordered dose to the safe dose range.The ordered dose is 20 mg, which falls within the safe dose range (15.91 mg to 31.82 mg). The ordered dose is safe.

Step 4: Calculate the amount needed based on the ordered dose.Volume required=20 mg50 mg/ml=0.4 ml\text{Volume required} = \frac{20 \text{ mg}}{50 \text{ mg/ml}} = 0.4 \text{ ml}Volume required=50 mg/ml20 mg​=0.4 ml

4. Vancomycin (Vancocin)

  • Order: 54 mg IV Q 8 hours in 12 ml D5 ¼ NS for a 5.5 kg infant.
  • Safe dose: 10 mg/kg/dose Q 8 hours.
  • Stock concentration after reconstitution: 50 mg/ml.

Step 1: Calculate the safe dose per administration.Safe dose=10 mg/kg/dose×5.5 kg=55 mg\text{Safe dose} = 10 \text{ mg/kg/dose} \times 5.5 \text{ kg} = 55 \text{ mg}Safe dose=10 mg/kg/dose×5.5 kg=55 mg

Step 2: Compare the ordered dose to the safe dose.The ordered dose is 54 mg, which is slightly less than the safe dose of 55 mg. The ordered dose is safe.

Step 3: Calculate the amount needed based on the ordered dose.Volume required=54 mg50 mg/ml=1.08 ml\text{Volume required} = \frac{54 \text{ mg}}{50 \text{ mg/ml}} = 1.08 \text{ ml}Volume required=50 mg/ml54 mg​=1.08 ml

5. Phytonadione (Vitamin K)

  • Order: 1 mg IM X 1 dose for a 4 kg newborn.
  • Safe dose: 0.5-1.0 mg/dose IM, SQ, IV X 1.
  • Stock concentration: 10 mg/ml.

Step 1: Confirm the dose is within the safe range.The ordered dose is 1 mg, which is within the safe dose range (0.5-1.0 mg). The ordered dose is safe.

Step 2: Calculate the amount needed based on the ordered dose.Volume required=1 mg10 mg/ml=0.1 ml\text{Volume required} = \frac{1 \text{ mg}}{10 \text{ mg/ml}} = 0.1 \text{ ml}Volume required=10 mg/ml1 mg​=0.1 ml

Summary:

  1. Theophylline: 12.19 ml required; dose is not safe.
  2. Ceftazidime: 2.95 ml required; dose is safe.
  3. Meperidine HCL: 0.4 ml required; dose is safe.
  4. Vancomycin: 1.08 ml required; dose is safe.
  5. Phytonadione: 0.1 ml required; dose is safe.