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 inequality that represents the number of half-hour appointments, x, and the number of 45-minute appointments, y, the doctor may have in a week is:
30x + 45y ≤ 35 hours.
The number of half-hour appointments is represented by "x" and the number of 45-minute appointments is represented by "y". Since the doctor limits the appointments to at most 35 hours per week, we can write the inequality:
30x + 45y ≤ 35 * 60
This inequality states that the total time taken by half-hour appointments (30x) and 45-minute appointments (45y) should be less than or equal to 35 hours (35 * 60 minutes).
To 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, we need to consider the time allocated for each type of appointment and the total number of hours available.
Let's break down the information given:
- A half-hour appointment takes 0.5 hours.
- A 45-minute appointment takes 0.75 hours (45 minutes = 0.75 hours).
- The doctor limits total appointments to, at most, 35 hours per week.
Based on this, let's write the inequality:
0.5x + 0.75y ≤ 35
In this inequality, 0.5x represents the total hours spent on half-hour appointments, and 0.75y represents the total hours spent on 45-minute appointments. The sum of these should be less than or equal to 35, the maximum number of hours the doctor can allocate per week.