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 twice 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 spends 4 * 2 = <<4*2=8>>8 hours in class a week.
She spends 8 + 8 = <<8+8=16>>16 hours on class and homework.
She spends 7 * 8 = <<7*8=56>>56 hours sleeping each week.
Thus, Lisa only has 168 - 16 - 56 = <<168-16-56=96>>96 hours of her free time left.
That means she can work at most 96 hours each week. Answer: \boxed{96}.
To determine the maximum amount of time Lisa can work each week, we need to subtract the time she spends on sleep, homework, and class from the total hours in a week.
Let's break it down:
Total hours in a week: 168 hours
Hours for sleep: 8 hours/night x 7 nights = 56 hours
Hours for homework: 21 hours/week
Hours for class: 4 hours/class x 2 classes = 8 hours
Now we can calculate the maximum working hours:
Max working hours = Total hours - (Sleep hours + Homework hours + Class hours)
Max working hours = 168 hours - (56 hours + 21 hours + 8 hours)
Max working hours = 168 hours - 85 hours
Max working hours = 83 hours
Therefore, Lisa can work at most 83 hours each week.
To determine the maximum amount of time Lisa can work each week, we need to calculate the total time she spends on classes, homework, sleep, and account for the total number of hours in a week.
Let's break it down:
1. Lisa spends 4 hours in each class, twice a week (on Tuesday and Thursday), so the total number of hours she spends in classes each week is 4 hours/class x 2 classes = 8 hours.
2. Lisa sets aside 21 hours for homework each week.
3. Lisa wants to ensure 8 hours of sleep each night, so the total number of hours she dedicates to sleep each week is 8 hours/night x 7 nights = 56 hours.
4. We know that there are 168 hours in one week.
Now, let's write an inequality to represent the maximum amount of time Lisa can work each week:
Total time for classes + Total time for homework + Total time for sleep + Total time for work ≤ Total number of hours in a week
8 hours + 21 hours + 56 hours + Total time for work ≤ 168 hours
85 hours + Total time for work ≤ 168 hours
To determine the maximum time Lisa can work, we rearrange the inequality:
Total time for work ≤ 168 hours - 85 hours
Total time for work ≤ 83 hours
Therefore, Lisa can work a maximum of 83 hours each week.