A patient is prescribed 100.0 mg/day of antibiotic for 2 weeks. The antibiotic is available in vials that contain 20.0 mg/vial of the drug. How many vials are necessary for the entire treatment?
The Correct Answer and Explanation is:
To determine how many vials of the antibiotic are needed for the entire treatment, we can break the problem down into two steps:
Step 1: Calculate the total dosage required for the entire treatment
The patient is prescribed 100.0 mg of the antibiotic per day for 2 weeks. First, we need to figure out the total dosage for the entire treatment: Total dosage=Dosage per day×Number of days\text{Total dosage} = \text{Dosage per day} \times \text{Number of days}Total dosage=Dosage per day×Number of days
Given that there are 7 days in a week, 2 weeks would have: 2 weeks=14 days2 \, \text{weeks} = 14 \, \text{days}2weeks=14days
Now, multiply the daily dosage (100.0 mg) by 14 days: Total dosage=100.0 mg/day×14 days=1400.0 mg\text{Total dosage} = 100.0 \, \text{mg/day} \times 14 \, \text{days} = 1400.0 \, \text{mg}Total dosage=100.0mg/day×14days=1400.0mg
So, the patient requires 1400.0 mg of the antibiotic for the entire 2-week treatment.
Step 2: Determine the number of vials required
Next, we calculate how many vials of the antibiotic are needed. Each vial contains 20.0 mg of the drug. To find out how many vials are needed, divide the total required dosage by the dosage per vial: Number of vials=Total dosageDosage per vial=1400.0 mg20.0 mg/vial=70.0 vials\text{Number of vials} = \frac{\text{Total dosage}}{\text{Dosage per vial}} = \frac{1400.0 \, \text{mg}}{20.0 \, \text{mg/vial}} = 70.0 \, \text{vials}Number of vials=Dosage per vialTotal dosage=20.0mg/vial1400.0mg=70.0vials
Final Answer:
The patient will need 70 vials of the antibiotic for the entire 2-week treatment.
This calculation assumes that the patient takes the full prescribed dosage each day without any loss or error in measurement. Additionally, you should always double-check with a healthcare provider or pharmacist to confirm the correct dosage and quantity required.
