Answer:
To represent the number of half-hour appointments, x, and the number of 45-minute appointments, y, the doctor may have in a week, you can use the following inequality based on the time constraint of 35 hours per week:
0.5x + 0.75y ≤ 35
Here's how we arrive at this inequality step by step:
The doctor schedules half-hour appointments, which means each half-hour appointment takes 0.5 hours.
The doctor also schedules 45-minute appointments, which means each 45-minute appointment takes 0.75 hours (since there are 60 minutes in an hour).
To find the total hours spent on half-hour appointments, you multiply the number of half-hour appointments (x) by 0.5.
To find the total hours spent on 45-minute appointments, you multiply the number of 45-minute appointments (y) by 0.75.
The total hours spent on both types of appointments (half-hour and 45-minute) should not exceed the doctor's limit of 35 hours per week.
Therefore, the sum of the hours spent on half-hour appointments (0.5x) and the hours spent on 45-minute appointments (0.75y) should be less than or equal to 35 hours, which leads to the inequality: 0.5x + 0.75y ≤ 35.
This inequality represents the doctor's scheduling constraint, ensuring that the total time spent on appointments in a week does not exceed 35 hours.
Explanation:
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