Adoctors office schedules 15 minute appointments and half hour appointments for weekdays the doctor limits his appointments two at most 30 hours per week right in any quality to represent the number of 15 minute appointments x in the number of half hour appointments y the doctor may have been a week

x + 2y ≤ 120

Explanation:

1) Number of 15-minutes appointment: x

2) Time in hours spent in x appointmens: 15x/60 = x/4

3) Number of 30-minutes appointment:  y

4) Time in hours spent in y appointmens: 30y/60 = y/2

5) Time in hours spent in both x and y appointments: x/4 + y/2

6) Limit of hours per week = 30 ⇒ x/4 + y/2 ≤ 30

7) Simplify the inequality.

Multiply both sides by 4:

x + 2y ≤ 120