This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Question 1 (a) Step 1: Calculate Eli's daily dose of erythromycin. Formula: Daily dose = dose per kg per day × body weight Eli's body weight = 50 kg (12-year-old child) Dose = 5 mg/kg/day Daily dose = 5 mg/kg/day × 50 kg = 250 mg/day Step 2: Calculate concentration of suspension. Formula: Concentration = mg per 5 ml5 ml Concentration = 125 mg5 ml = 25 mg/ml Step 3: Calculate total drug in the bottle. Formula: Total drug = concentration × volume of bottle Total drug = 25 mg/ml × 200 ml = 5000 mg Step 4: Calculate how many days the bottle will last. Formula: Days = total drugdaily dose Days = 5000 mg250 mg/day = 20 days The bottle will last 20 days. 20 days Question 1 (b) James is prescribed 50 mg oral qid for 5 days. Assume 50 mg tablets. Step 1: Calculate daily dose. qid = 4 doses per day Daily dose = 50 mg/dose × 4 doses/day = 200 mg/day Step 2: Calculate total dose for 5 days. Total dose = 200 mg/day × 5 days = 1000 mg Step 3: Calculate number of tablets. Formula: Number of tablets = total dosemg per tablet Number of tablets = 1000 mg50 mg/tablet = 20 tablets Drew/James needs 20 tablets for the complete course. 20 Question 1 (c) Assume: Patient receiving 500 ml serum IV over 10 hours. Drop factor = 20 drops/ml. Calculate drops per minute. Step 1: Calculate total infusion time in minutes. Time = 10 hours × 60 min/hour = 600 min Step 2: Calculate infusion rate in ml/min. Formula: ml/min = total volumetotal time ml/min = 500 ml600 min = (5)/(6) ml/min ≈ 0.833 ml/min Step 3: Calculate drops per minute. Formula: gtt/min = ml/min × drop factor gtt/min = (5)/(6) ml/min × 20 drops/ml = (100)/(6) gtt/min ≈ 16.7 gtt/min Set the drip rate to 17 gtt/min (rounded). 17 gtt/min Question 1 (d) Assume: The 500 ml serum contains 1000 mg drug (e.g., 1 g), infused over 10 hours. Calculate mg/min. Step 1: Concentration of drug. Formula: Conc. = total drugvolume Conc. = 1000 mg500 ml = 2 mg/ml Step 2: Drug delivery rate. From (c), ml/min = (5)/(6) ml/min mg/min = 2 mg/ml × (5)/(6) ml/min = (10)/(6) mg/min ≈ 1.67 mg/min Lucy receives 1.67 mg/min. 1.67 mg/min Question 1 (e) From (b), daily tablets for James = 200 mg/day50 mg/tablet = 4 tablets/day Number of tablets taken every day: 4 4