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's two classes take up a total of 4 hours on Tuesday and 4 hours on Thursday, so they take up a total of 4+4 = <<4+4=8>>8 hours in a week.
She sets aside 21 hours for homework, so that leaves her with 168 - 8 - 21 = <<168-8-21=139>>139 hours for the rest of the week.
She wants to ensure 8 hours of sleep each night, so that takes up 8 x 7 = <<8*7=56>>56 hours in a week.
That leaves her with 139 - 56 = <<139-56=83>>83 hours for the rest of the week.
She wants to work the maximum amount of time possible, so she needs to ensure that she has enough time for all her other activities.
Therefore, the maximum amount of time she can work each week is 83 hours. Answer: \boxed{83}.
To calculate the maximum amount of time Lisa can work each week, we need to consider her commitments and determine how many hours are left after accounting for those commitments.
First, let's calculate the total amount of time Lisa spends on her classes each week. Since each class is 4 hours long and she has two classes, the total time spent on classes per week is 4 * 2 = 8 hours.
Next, let's calculate the total amount of time Lisa spends on sleep each week. Since she wants 8 hours of sleep each night and there are 7 nights in a week, the total time spent on sleep per week is 8 * 7 = 56 hours.
We also know that Lisa sets aside 21 hours for homework each week.
Now let's calculate the total time spent on classes, sleep, and homework combined: 8 (class hours) + 56 (sleep hours) + 21 (homework hours) = 85 hours.
Since there are 168 hours in one week, we can find the maximum amount of time Lisa can work by subtracting the time spent on classes, sleep, and homework from the total number of hours in a week: 168 - 85 = 83 hours.
Therefore, the maximum amount of time Lisa can work each week is 83 hours.
To write an inequality for this situation, let's assume the maximum amount of time Lisa can work each week is W hours. The inequality can be expressed as:
W ≤ 83
To determine the maximum amount of time Lisa can work each week, we need to calculate the total amount of time she spends on her classes, sleep, and homework, and then subtract that from the total number of hours in a week.
Lisa has two classes, each lasting 4 hours, so the total time spent in classes each week is:
2 classes x 4 hours/class = 8 hours/week
She also sets aside 21 hours for homework each week.
Lisa wants to ensure 8 hours of sleep each night, so the total time spent on sleep each week is:
8 hours/night x 7 nights/week = 56 hours/week
Adding up the time spent on classes, homework, and sleep, we get:
8 hours (classes) + 21 hours (homework) + 56 hours (sleep) = 85 hours/week
Now, we subtract the total time spent on these activities from the total number of hours in a week:
168 hours (total week hours) - 85 hours (classes, homework, sleep) = 83 hours
So, Lisa can work at most 83 hours each week.
To write the inequality, let x represent the maximum number of hours Lisa can work each week. We can then write the equation:
x ≤ 83
This is because Lisa's work hours cannot exceed the total hours available (83 hours).
Note: The inequality is written with ≤ instead of = because Lisa can work less than or equal to 83 hours, but not more.