The dosage of quinine when a $145-lb$ adult takes a $200.-mg$ tablet is weight. How many $\mu g$ of drug per kg of body?
A. 15.2
B. $1.60 \times 10^3$
C. $4.41 \times 10^5$
D. $1.38 \times 10^6$
E. $3.04 \times 10^3$
Answer (2)
Convert the adult's weight from pounds to kilograms: 145 lb × 0.453592 lb kg = 65.77084 kg .
Convert the tablet dosage from milligrams to micrograms: 200 mg × 1000 mg μg = 200000 μg .
Calculate the dosage in μg / k g : 65.77084 kg 200000 μg = 3040.861269 kg μg .
The dosage is approximately 3.04 × 1 0 3 μg / k g .
Explanation
Problem Analysis We are asked to find the dosage of quinine in μg per kg of body weight, given that a 145-lb adult takes a 200-mg tablet.
Weight Conversion First, we need to convert the adult's weight from pounds (lb) to kilograms (kg). We know that 1 lb = 0.453592 kg. Therefore, the weight in kg is: W k g = 145 lb × 0.453592 lb kg = 65.77084 kg .
Dosage Conversion Next, we need to convert the tablet dosage from milligrams (mg) to micrograms ( μg ). We know that 1 mg = 1000 μg . Therefore, the dosage in μg is: D μg = 200 mg × 1000 mg μg = 200000 μg .
Dosage Calculation Now, we can calculate the dosage in μg / k g by dividing the dosage in μg by the weight in kg: Dosage = W k g D μg = 65.77084 kg 200000 μg = 3040.861269 kg μg .
Final Answer Rounding to one decimal place, the dosage is approximately 3040.9 μg / k g . The closest answer choice is 3.04 × 1 0 3 μg / k g .
Examples
Understanding drug dosages is crucial in healthcare. For instance, calculating the correct antibiotic dosage for a child based on their weight ensures effective treatment while minimizing the risk of side effects. Similarly, in veterinary medicine, accurate dosage calculations are essential for treating animals of different sizes and species. This problem demonstrates the importance of unit conversions and proportional reasoning in real-world medical scenarios.
The dosage of quinine for a 145-lb adult taking a 200-mg tablet is calculated to be approximately 3.04 × 1 0 3 μg / k g after converting body weight to kg and the dosage to micrograms. The appropriate multiple-choice answer is E. 3.04 × 1 0 3 .
;
