Weight-Based Dosing - Pharmacology

1. A 176-lb patient is receiving a continuous intravenous infusion at a rate of 15 mL/hr. The infusion bag is labeled "Drug X 500 mg in 250 mL of NS". What dose is the patient receiving in mg/kg/hr?
   Answer: 0.38 mg/kg/hr First, convert the patient's weight to kg: $176 \text{ lbs} \div 2.2 \text{ lbs/kg} = 80 \text{ kg}$. Second, determine the concentration of the drug: $500 \text{ mg} \div 250 \text{ mL} = 2 \text{ mg/mL}$. Third, calculate the rate of drug administration in mg/hr: $15 \text{ mL/hr} \times 2 \text{ mg/mL} = 30 \text{ mg/hr}$. Finally, normalize this rate to the patient's weight: $30 \text{ mg/hr} \div 80 \text{ kg} = 0.375 \text{ mg/kg/hr}$, which rounds to 0.38 mg/kg/hr.
2. An infant weighs 8.8 lbs and requires an antibiotic at a dose of 25 mg/kg/day, divided into two doses. The oral suspension is available at a concentration of 125 mg/5 mL. What volume in mL is needed for a single morning dose?
   Answer: 2.0 mL First, convert the infant's weight to kg: $8.8 \text{ lbs} \div 2.2 \text{ lbs/kg} = 4 \text{ kg}$. Second, calculate the total daily dose: $4 \text{ kg} \times 25 \text{ mg/kg/day} = 100 \text{ mg/day}$. Third, determine the amount for a single dose: $100 \text{ mg/day} \div 2 \text{ doses} = 50 \text{ mg/dose}$. Finally, calculate the volume of the suspension. The concentration is $125 \text{ mg}/5 \text{ mL}$, which simplifies to $25 \text{ mg/mL}$. The volume is $50 \text{ mg} \div 25 \text{ mg/mL} = 2.0 \text{ mL}$.
3. A 3-year-old child weighing 15 kg is prescribed ceftriaxone 50 mg/kg IM as a single dose. The medication is available as a 1 g vial of powder. The reconstitution instructions state: "Add 3.6 mL of sterile water to yield a final concentration of 250 mg/mL." What volume of the reconstituted solution should be drawn up for administration?
   Answer: 3.0 mL First, calculate the required dose in mg: $15 \text{ kg} \times 50 \text{ mg/kg} = 750 \text{ mg}$. The problem provides the final concentration of the reconstituted solution, which is 250 mg/mL. The volume of diluent added (3.6 mL) and the total vial size (1 g) are relevant for preparation but not for the final volume calculation once concentration is known. Calculate the volume to administer using the final concentration: $750 \text{ mg} \div 250 \text{ mg/mL} = 3.0 \text{ mL}$.
4. An 80-kg patient receives an initial IV push dose of an antiarrhythmic drug at 0.5 mg/kg. The order states, "If arrhythmia persists, increase dose by 20% for the next administration." If the patient's arrhythmia persists, what will be the new dose in mg?
   Answer: 48 mg First, calculate the initial dose administered: $80 \text{ kg} \times 0.5 \text{ mg/kg} = 40 \text{ mg}$. Next, calculate the 20% increase: $40 \text{ mg} \times 0.20 = 8 \text{ mg}$. The new dose is the initial dose plus the increase: $40 \text{ mg} + 8 \text{ mg} = 48 \text{ mg}$. Alternatively, one can calculate the new dose directly: $40 \text{ mg} \times 1.20 = 48 \text{ mg}$.
5. A patient weighing 60 kg is prescribed a chemotherapy agent at a dose of 30 mg/m². The patient's Body Surface Area (BSA) is calculated to be 1.7 m². The order specifies that if the weight-based dose of 50 mg/kg exceeds the BSA-based dose, the lower of the two should be administered. Which dose should the patient receive?
   Answer: 51 mg This question requires calculating two different potential doses and then comparing them based on the provided rule. First, calculate the BSA-based dose: $1.7 \text{ m}^2 \times 30 \text{ mg/m}^2 = 51 \text{ mg}$. Second, calculate the weight-based dose: $60 \text{ kg} \times 50 \text{ mg/kg} = 3000 \text{ mg}$. The order specifies administering the lower of the two doses. Comparing the two calculated doses, 51 mg is lower than 3000 mg. Therefore, the patient should receive 51 mg. The BSA is already provided, so height is not needed.
6. A 198-lb patient requires a heparin bolus of 80 units/kg followed by a continuous infusion. The pharmacy stocks heparin vials containing 5,000 units/mL. What volume of heparin should be administered for the bolus dose?
   Answer: 1.44 mL First, convert the patient's weight to kg: $198 \text{ lbs} \div 2.2 \text{ lbs/kg} = 90 \text{ kg}$. Second, calculate the total number of units for the bolus dose: $90 \text{ kg} \times 80 \text{ units/kg} = 7200 \text{ units}$. Finally, calculate the volume to be administered using the available concentration: $7200 \text{ units} \div 5000 \text{ units/mL} = 1.44 \text{ mL}$.
7. A 90-kg patient is prescribed a medication with a recommended dose of 2-4 mg/kg/day. The physician orders 150 mg PO BID. Which of the following is the most accurate assessment of the prescribed mg/kg/day dose?
   Answer: 3.3 mg/kg/day, which is within the therapeutic range. When you encounter dosage calculation questions, you need to systematically convert the prescribed dose to mg/kg/day and compare it to the therapeutic range. Start by calculating the total daily dose. The prescription is 150 mg PO BID (twice daily), so: $150 \text{ mg} \times 2 = 300 \text{ mg/day}$ Next, convert this to mg/kg/day by dividing by the patient's weight: $\frac{300 \text{ mg/day}}{90 \text{ kg}} = 3.33 \text{ mg/kg/day}$ This rounds to 3.3 mg/kg/day, which falls within the recommended therapeutic range of 2-4 mg/kg/day, making answer D correct. Let's examine why the other options are wrong. Answer A (1.7 mg/kg/day) represents a calculation error—likely dividing 150 mg by 90 kg without accounting for the BID dosing, missing half the daily dose. Answer B (6.6 mg/kg/day) suggests another calculation mistake, possibly multiplying instead of dividing somewhere in the process. Answer C (4.2 mg/kg/day) is close but mathematically incorrect—it might result from rounding errors or misreading the patient's weight. The key strategy here is methodical calculation: always identify the total daily dose first (accounting for dosing frequency), then divide by patient weight, and finally compare to the therapeutic range. Double-check your arithmetic, as dosage calculations are prone to simple mathematical errors that can lead to dangerous clinical consequences. Remember that BID means twice daily, TID means three times daily, and QID means four times daily.
8. The physician orders a loading dose of 6 mg/kg based on IBW. Using the provided information, what is the correct loading dose to prepare?
   Answer: 342 mg First, calculate the patient's height in inches. $165 \text{ cm} \div 2.54 \text{ cm/in} \approx 65 \text{ inches}$. Since 5 feet is 60 inches, the patient is 5 inches over 5 feet. Next, calculate the IBW using the provided formula: $45.5 \text{ kg} + (2.3 \text{ kg/in} \times 5 \text{ in}) = 45.5 \text{ kg} + 11.5 \text{ kg} = 57 \text{ kg}$. Finally, calculate the loading dose: $57 \text{ kg} \times 6 \text{ mg/kg} = 342 \text{ mg}$.
9. A patient weighing 80 kg is to receive a loading dose of phenytoin at 15 mg/kg. The medication is to be infused at a rate not exceeding 50 mg/min. What is the minimum duration, in minutes, for this infusion?
   Answer: 24 minutes When you encounter dosing calculations involving infusion rates, you need to determine the total dose required and then apply the maximum safe infusion rate to find the minimum time needed. First, calculate the total loading dose: $80 \text{ kg} \times 15 \text{ mg/kg} = 1200 \text{ mg}$ Next, apply the maximum infusion rate constraint. Since phenytoin cannot be infused faster than 50 mg/min, divide the total dose by this rate: $\frac{1200 \text{ mg}}{50 \text{ mg/min}} = 24 \text{ minutes}$ This gives you the minimum safe duration for the infusion. Looking at the wrong answers: A) 16 minutes would require an infusion rate of 75 mg/min (1200 ÷ 16), which exceeds the 50 mg/min safety limit and could cause cardiovascular toxicity. B) 48 minutes represents a calculation error where someone might have doubled the correct answer or miscalculated the dose as 2400 mg. C) 30 minutes would only deliver 1500 mg total if infusing at maximum rate, suggesting confusion about the dose calculation. Answer D) 24 minutes correctly respects both the prescribed dose (1200 mg) and the safety constraint (≤50 mg/min). Study tip: For IV medication calculations, always work through three steps: calculate total dose needed, identify the rate limitation, then solve for time using the formula Time = Total Dose ÷ Maximum Rate. This systematic approach prevents errors and ensures patient safety parameters are respected.
10. A 154-lb patient requires amikacin at a dose of 15 mg/kg/day, administered in two equally divided doses. The pharmacy supplies amikacin in vials with a concentration of 500 mg/2 mL. How many milliliters should be administered for a single dose?
    Answer: 2.1 mL This is a multi-step calculation. First, convert the patient's weight from pounds (lbs) to kilograms (kg): $154 \text{ lbs} \div 2.2 \text{ lbs/kg} = 70 \text{ kg}$. Second, calculate the total daily dose in mg: $70 \text{ kg} \times 15 \text{ mg/kg/day} = 1050 \text{ mg/day}$. Third, determine the single dose amount, as the total daily dose is divided into two doses: $1050 \text{ mg} \div 2 = 525 \text{ mg}$. Finally, calculate the volume to administer based on the available concentration (500 mg/2 mL, which is 250 mg/mL): $525 \text{ mg} \div 250 \text{ mg/mL} = 2.1 \text{ mL}$.
11. A 70-kg patient with normal renal function is ordered enoxaparin for DVT prophylaxis at a dose of 1 mg/kg subcutaneously every 12 hours. The pharmacy dispenses pre-filled syringes of 80 mg/0.8 mL. How should the dose be administered?
    Answer: Administer 0.7 mL from the syringe. First, calculate the required dose for the patient: $70 \text{ kg} \times 1 \text{ mg/kg} = 70 \text{ mg}$. Next, determine the concentration of the provided syringe: $80 \text{ mg} \div 0.8 \text{ mL} = 100 \text{ mg/mL}$. Now, calculate the volume needed to deliver the 70 mg dose: $70 \text{ mg} \div 100 \text{ mg/mL} = 0.7 \text{ mL}$. Therefore, 0.7 mL should be administered from the 80 mg/0.8 mL syringe. While requesting an exact dose syringe might be an option in some institutions, the question asks how the dose should be administered from the supplied syringe.
12. A neonate weighing 3.5 kg is prescribed a once-daily medication at a dose of 15 mcg/kg. The drug is supplied in a solution with a concentration of 0.1 mg/mL. What volume, in mL, should be administered? Round to two decimal places.
    Answer: 0.53 mL First, calculate the total dose in mcg: $3.5 \text{ kg} \times 15 \text{ mcg/kg} = 52.5 \text{ mcg}$. Second, convert the dose from mcg to mg to match the concentration unit: $52.5 \text{ mcg} \div 1000 \text{ mcg/mg} = 0.0525 \text{ mg}$. Third, calculate the volume to administer: $0.0525 \text{ mg} \div 0.1 \text{ mg/mL} = 0.525 \text{ mL}$. Finally, round the result to two decimal places as instructed, which gives 0.53 mL.
13. A 50-kg patient is prescribed Drug Z at 4 mg/kg/day. The drug's half-life requires it to be given in 4 divided doses. The drug is supplied as 50 mg tablets that can be split in half. How many tablets should be administered per dose?
    Answer: One tablet Dosage calculations in pharmacology require you to work systematically through total daily dose, individual dose amounts, and finally tablet quantities. This type of problem tests your ability to convert between different units while accounting for drug formulation. Let's calculate step by step. First, determine the total daily dose: 50 kg × 4 mg/kg/day = 200 mg/day. Since the drug is given in 4 divided doses throughout the day, each individual dose is 200 mg ÷ 4 = 50 mg per dose. Finally, convert to tablets: with 50 mg tablets available, you need 50 mg ÷ 50 mg/tablet = 1 tablet per dose. Now let's examine why the other options are incorrect. Choice A (one-half tablet) would only provide 25 mg per dose, giving a total daily dose of 100 mg—half of what's prescribed. Choice B (two tablets) would deliver 100 mg per dose, resulting in 400 mg daily, which is double the intended dose and potentially toxic. Choice C (one and one-half tablets) would provide 75 mg per dose for a total of 300 mg daily, which is 50% higher than prescribed. Choice D (one tablet) correctly provides exactly 50 mg per dose and 200 mg daily as prescribed. Study tip: Always work through dosage calculations in order: patient weight × dose per kg = total daily dose, then divide by frequency for individual dose, then convert to available tablet strength. Double-check your math by working backward—does your final answer multiplied by frequency equal the intended daily dose?
14. A 75-kg male with a severe infection is to be started on gentamicin. The hospital protocol calls for a loading dose of 2 mg/kg, followed by a maintenance dose of 5 mg/kg/day administered in three divided doses. The loading dose is to be diluted in 100 mL NS and infused over 30 minutes. What is the total amount of gentamicin in mg that should be prepared for the initial infusion?
    Answer: 150 mg The question asks for the amount of drug for the initial infusion, which corresponds to the loading dose. The maintenance dose information is extraneous to this specific question. Calculate the loading dose: $75 \text{ kg} \times 2 \text{ mg/kg} = 150 \text{ mg}$.
15. A 10-year-old male weighing 121 lbs is prescribed intravenous vancomycin. The standard pediatric dose is 60 mg/kg/day, divided every 6 hours. However, the absolute maximum daily dose for this medication is 3 g/day. What is the appropriate single dose in mg to administer?
    Answer: 750 mg First, convert the patient's weight to kg: $121 \text{ lbs} \div 2.2 \text{ lbs/kg} = 55 \text{ kg}$. Next, calculate the theoretical total daily dose based on weight: $55 \text{ kg} \times 60 \text{ mg/kg/day} = 3300 \text{ mg/day}$. This dose (3.3 g/day) exceeds the specified absolute maximum daily dose of 3 g/day (3000 mg/day). Therefore, the dose must be capped at 3000 mg/day. Since the medication is administered every 6 hours (4 times a day), the single dose is: $3000 \text{ mg/day} \div 4 \text{ doses} = 750 \text{ mg/dose}$.
16. A 25-kg child is prescribed an antibiotic with a recommended dose of 20-40 mg/kg/day, given in divided doses every 8 hours. The physician orders 150 mg every 8 hours. Which statement accurately assesses the appropriateness of this ordered dose?
    Answer: The dose is too low, as the total daily dose is below the minimum recommended daily dose. First, calculate the safe therapeutic range for the total daily dose. Minimum daily dose: $25 \text{ kg} \times 20 \text{ mg/kg/day} = 500 \text{ mg/day}$. Maximum daily dose: $25 \text{ kg} \times 40 \text{ mg/kg/day} = 1000 \text{ mg/day}$. Next, calculate the total daily dose the patient is actually receiving: $150 \text{ mg/dose} \times 3 \text{ doses/day} = 450 \text{ mg/day}$. Comparing the ordered daily dose (450 mg) to the recommended range (500-1000 mg), the ordered dose is below the minimum therapeutic threshold.
17. A 110-lb patient is ordered IV acyclovir at 10 mg/kg/dose every 8 hours. The medication is supplied in a 500 mg/10 mL vial. The dose must be diluted in 100 mL of normal saline and infused over 1 hour. What volume of acyclovir from the vial should be added to the 100 mL bag of NS?
    Answer: 10.0 mL When you encounter IV medication dosing questions, you need to work through three key calculations: patient weight conversion, dose calculation, and volume extraction from the vial. First, convert the patient's weight from pounds to kilograms: $110 \text{ lb} \div 2.2 = 50 \text{ kg}$. Next, calculate the required dose: $50 \text{ kg} \times 10 \text{ mg/kg} = 500 \text{ mg}$. Finally, determine what volume contains this dose from the available vial concentration of 500 mg/10 mL: $\frac{500 \text{ mg}}{500 \text{ mg/10 mL}} = 10 \text{ mL}$. The correct answer is D) 10.0 mL because you need exactly 500 mg of acyclovir, and the vial contains 50 mg/mL, requiring 10 mL total. Choice A) 5.0 mL represents a calculation error where someone might have divided the final dose by 100 instead of using the vial concentration properly. Choice B) 22.0 mL suggests confusion with the weight conversion - this might result from using 110 instead of 50 in the dose calculation. Choice C) 11.0 mL could occur if someone incorrectly rounded the weight conversion or made an arithmetic error in the final volume calculation. Remember the systematic approach for IV dosing problems: convert weight to kg, multiply by mg/kg dose, then use the vial concentration to find the required volume. Always double-check your weight conversion (divide by 2.2) and ensure your final volume makes sense relative to the vial size.
18. A 165-lb patient in the ICU is receiving a norepinephrine infusion prepared as 4 mg in 250 mL of D5W. The current infusion rate is 21 mL/hr. What is the current dose the patient is receiving in mcg/kg/min?
    Answer: 0.07 mcg/kg/min This multi-step problem requires working backward. First, convert weight: $165 \text{ lbs} \div 2.2 = 75 \text{ kg}$. Second, find the drug concentration: $4 \text{ mg} \div 250 \text{ mL} = 0.016 \text{ mg/mL}$. Convert concentration to mcg/mL: $0.016 \text{ mg/mL} \times 1000 = 16 \text{ mcg/mL}$. Third, calculate the dose rate in mcg/hr: $21 \text{ mL/hr} \times 16 \text{ mcg/mL} = 336 \text{ mcg/hr}$. Fourth, convert the rate to mcg/min: $336 \text{ mcg/hr} \div 60 \text{ min/hr} = 5.6 \text{ mcg/min}$. Finally, normalize to patient weight: $5.6 \text{ mcg/min} \div 75 \text{ kg} \approx 0.075 \text{ mcg/kg/min}$, which rounds to 0.07 mcg/kg/min.
19. A 68-kg patient requires a dobutamine infusion at a rate of 5 mcg/kg/min. The pharmacy prepares an infusion bag containing 250 mg of dobutamine in 250 mL of D5W. At what rate, in mL/hr, should the infusion pump be set?
    Answer: 20.4 mL/hr First, calculate the patient's dose in mcg/min: $5 \text{ mcg/kg/min} \times 68 \text{ kg} = 340 \text{ mcg/min}$. Next, convert this rate to mg/hr: $340 \frac{\text{mcg}}{\text{min}} \times \frac{1 \text{ mg}}{1000 \text{ mcg}} \times \frac{60 \text{ min}}{1 \text{ hr}} = 20.4 \text{ mg/hr}$. Then, determine the concentration of the solution: $250 \text{ mg} \div 250 \text{ mL} = 1 \text{ mg/mL}$. Finally, calculate the infusion rate in mL/hr: $\frac{20.4 \text{ mg/hr}}{1 \text{ mg/mL}} = 20.4 \text{ mL/hr}$.

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