Final answer:
To find the number of patients the dentist sees in a year, calculate the number of patients he sees in a week and multiply it by the number of weeks he works in a year, excluding vacation.
Step-by-step explanation:
To find the number of patients the dentist sees in a year, we need to calculate the number of patients he sees in a week first. In a 60-hour workweek, if he sees a patient every 20 minutes, he sees 60/20 = 3 patients per hour. Therefore, he sees 3 patients per hour * 60 hours per week = 180 patients per week.
Next, we need to calculate the number of weeks he works in a year. He works an average of 60 hours per week, so in a year, he works 60 hours per week * 52 weeks = 3120 hours.
Considering he takes 3 weeks vacation, the number of weeks he works in a year is 52 weeks - 3 weeks = 49 weeks. Now, we can calculate the number of patients he sees in a year: 180 patients per week * 49 weeks = 8820 patients.