Can someone explain how to solve this problem.
A doctors office schedules 15 min appointments and half hour appointments for weekdays. The docyor limits these appointments to, at most, 30 hours per week. Write an inequality to represent the number of 15 minute appointments x and the number of half hour appointments y the doctor may have in a week?
To solve this problem, we need to consider the time taken by each type of appointment (15-minute and half-hour) and the total time available for appointments in a week.
Let's break it down step by step:
1. Determine the time taken by each 15-minute appointment: Since each appointment lasts for 15 minutes, the total time taken for x 15-minute appointments would be 15x minutes.
2. Determine the time taken by each half-hour appointment: Since each appointment lasts for 30 minutes, the total time taken for y half-hour appointments would be 30y minutes.
3. Calculate the total time taken for all appointments: To find the total time taken for both types of appointments, we add the time taken for 15-minute appointments and the time taken for half-hour appointments. This can be represented by the inequality:
15x + 30y ≤ 30 hours
Note that we convert the time to hours, as the constraint is given to be in hours.
Important to note: The inequality includes the less than or equal to symbol (≤) since the doctor limits the appointments to at most 30 hours per week.
So, the inequality that represents the number of 15-minute appointments (x) and the number of half-hour appointments (y) the doctor may have in a week is: 15x + 30y ≤ 30 hours.