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.
The two classes meet 4 hours per session, twice a week, for a total of 4 * 2 = <<4*2=8>>8 hours per week.
She spends 8 hours a week on each class, so a total of 8 + 8 = <<8+8=16>>16 hours per week.
She sets aside 21 hours for homework, so she has 168 - 21 = <<168-21=147>>147 hours left.
She wants 8 hours of sleep each night, so she sleeps 8 * 7 = <<8*7=56>>56 hours per week.
She spends 56 hours sleeping and 16 hours on class and homework, so she has 147 - 56 - 16 = <<147-56-16=75>>75 hours left.
Therefore, the maximum number of hours she can work each week is 75 hours. Answer: \boxed{75}.
To determine the maximum number of hours Lisa can work each week, we need to understand how much time is already allocated for other activities, such as homework, classes, sleep, etc.
1. Total hours in a week: 168 hours
2. Hours allocated for homework:
- Lisa sets aside 21 hours a week for homework.
3. Hours allocated for classes:
- Each class is 4 hours long.
- Lisa's two classes meet twice a week (on Tuesday and Thursday).
- Total hours of classes each week: 4 hours/class × 2 classes × 2 meetings/week = 16 hours
4. Hours allocated for sleep:
- Lisa wants to ensure 8 hours of sleep each night.
- Total hours of sleep each week: 8 hours/night × 7 nights/week = 56 hours
5. Hours left for work:
- Total hours in a week - (hours allocated for homework + hours allocated for classes + hours allocated for sleep)
- 168 hours - (21 hours + 16 hours + 56 hours) = 75 hours
Thus, Lisa can work at most 75 hours each week.
To determine the maximum amount of time Lisa can work each week, we first need to calculate the total number of hours she has available for work after accounting for her classes, homework, and sleep.
The total number of hours in one week is 168.
The total number of hours she spends on classes is 4 hours/class * 2 classes = 8 hours.
The total number of hours she spends on homework is 21 hours.
The total number of hours she spends sleeping is 8 hours/night * 7 nights = 56 hours.
To find the maximum amount of time she can work each week, we subtract the time spent on classes, homework, and sleep from the total number of hours in one week:
168 hours - 8 hours (classes) - 21 hours (homework) - 56 hours (sleep) = 83 hours.
Therefore, the maximum amount of time Lisa can work each week is 83 hours.
We can also write this in equation form:
x ≤ 168 - 8 - 21 - 56
Simplifying the equation:
x ≤ 83
Therefore, Lisa can work at most 83 hours each week.