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------------------------------------------------ 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.

Lisa can theoretically work up to 83 hours a week. This calculation is based on subtracting her time committed to homework, classes, and sleep from the total hours in a week. However, practical considerations like time for meals, personal care, and leisure time are not accounted for in this calculation.

Explanation:

To resolve Lisa's problem, let's consider the time allocations she already has. First, she spends 21 hours a week for homework. Secondly, her classes are 4 hours each for a total of 8 hours in a week. Also, she has a requirement to have 8 hours of sleep each night which translates to 56 hours in a week (8 hours * 7 days).

So, if we sum up all these times: 21 (homework hours) + 8 (class hours) + 56 (sleep hours) = 85 hours. Lisa has already committed 85 hours in a week for these activities.

Now, keep in mind that there are 168 hours in a week. If we subtract the 85 hours (already committed) from the 168 hours (total hours in a week), we see that Lisa has 83 hours left in a week.

To write this in the form of inequality, we can say, let's W be the number of hours Lisa can work, we have:

0 <= W <= 83

Therefore, Lisa can work at most 83 hours per week. However, this does not include time for other essential activities like eating, personal care or leisure. Hence, while mathematically Lisa can work up to 83 hours a week, practically, it might be considerably less.

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