A doctor’s office schedules half-hour appointments and 45-minute appointments for weekdays. The doctor limits these appointments to, at most, 35 hours per week. Write an inequality to represent the number of half-hour appointments, x, and the number of 45-minute appointments, y, the doctor may have in a week.
The total time for half-hour appointments, in hours, is equal to 0.5x.
The total time for 45-minute appointments, in hours, is equal to (45/60)y = 0.75y.
Since the doctor limits the total appointment time to 35 hours per week, we can write the inequality as:
0.5x + 0.75y ≤ 35.
To write an inequality representing the number of half-hour appointments, x, and the number of 45-minute appointments, y, the doctor may have in a week, we need to consider the time limit of 35 hours.
One half-hour appointment takes 0.5 hours, while one 45-minute appointment takes 0.75 hours. Therefore, the total time spent on appointments can be expressed as:
0.5x + 0.75y
Since the doctor's limit is 35 hours per week, we can write the inequality as:
0.5x + 0.75y ≤ 35
To write an inequality to represent the number of half-hour appointments and 45-minute appointments the doctor may have in a week, we need to consider the time restrictions set by the doctor.
The doctor can schedule half-hour appointments and 45-minute appointments. We can assume there are a total of x half-hour appointments and y 45-minute appointments.
Since each half-hour appointment takes 30 minutes and each 45-minute appointment takes 45 minutes, the total time used by these appointments can be represented as:
Total time used by half-hour appointments = 30x
Total time used by 45-minute appointments = 45y
Now, the doctor limits the total appointments to, at most, 35 hours per week. Since there are 60 minutes in an hour, 35 hours is equal to 35 * 60 = 2100 minutes.
So, the total time used by the appointments should be less than or equal to 2100 minutes per week. Therefore, we can write the inequality as:
30x + 45y ≤ 2100
This inequality represents the limit on the number of half-hour appointments (x) and the number of 45-minute appointments (y) the doctor may have in a week.