Lisa is taking two classes at a local community college. She sets aside 21 hours for homework a week with these two classes. The two classes are 4 hours each once a week on Tuesday and Thursday. She wants to get a part-time job and ensure 8 hours of sleep each night. There are 168 hours in one week. How many hours can she work at most each week? Write and solve an inequality to determine the maximum amount of time she can work each week.

Answer 1

Let's break down Lisa's time commitments and determine the maximum amount of time she can work each week.

1. Lisa has 168 hours in a week.
2. She sets aside 21 hours for homework.
3. Her two classes each take 4 hours and are once a week on Tuesday and Thursday. So the total time for her classes is 4 hours * 2 classes = 8 hours per week.
4. She wants to ensure 8 hours of sleep each night, which is 8 hours * 7 days = 56 hours per week.
5. So far, Lisa's time commitments are 21 hours for homework + 8 hours for classes + 56 hours for sleep = 85 hours out of 168 available hours.
6. The remaining available hours are 168 hours - 85 hours = 83 hours.

Let's represent the maximum amount of time she can work each week as "x".

The inequality to represent this is:
x ≤ 83 hours

Therefore, Lisa can work at most 83 hours each week.