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SHOW ALL STEPS THAT YOU NEED TO SOLVE THIS PROBLEM. A doctor's office schedules half-hour appointments and 45-minute 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.

User Haseeb
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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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User Teerasej
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