Lisa is taking two classes 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 has 168-21 = <<168-21=147>>147 hours left in a week.
The two classes take 4*2 = <<4*2=8>>8 hours.
Lisa sleeps 8*7 = <<8*7=56>>56 hours in a week.
So, she has 147-8-56 = <<147-8-56=83>>83 hours left to work, sleep or do anything else.
Therefore, Lisa can work at most 83 hours each week. Answer: \boxed{83}.
To determine the maximum amount of time Lisa can work each week, we need to consider the time she spends on classes, homework, sleep, and the total number of hours in a week.
Hours spent on classes: 4 hours/class * 2 classes = 8 hours/week
Hours spent on homework: 21 hours/week
Hours spent sleeping: 8 hours/night * 7 nights = 56 hours/week
Total time spent on classes, homework, and sleep: 8 hours + 21 hours + 56 hours = 85 hours/week
Total time available in a week: 168 hours/week
To find the maximum amount of time Lisa can work, we subtract the time spent on classes, homework, and sleep from the total time available:
Maximum work hours = Total time available - Time spent on classes, homework, and sleep
Maximum work hours = 168 hours - 85 hours
Maximum work hours = 83 hours/week
So, Lisa can work at most 83 hours each week.
Inequality: Let "x" represent the number of hours Lisa can work each week.
x ≤ 83
Solution: The maximum amount of time Lisa can work each week is 83 hours or less.
To determine the maximum amount of time Lisa can work each week, we need to subtract the time she spends on homework, sleep, and classes from the total number of hours in a week (168 hours).
Let's break it down step by step:
1. Lisa spends 4 hours on each class, twice a week (Tuesday and Thursday). So the total time spent on classes is 4 hours + 4 hours = 8 hours.
2. Lisa also sets aside 21 hours for homework each week.
3. Lisa wants to ensure 8 hours of sleep each night, so she needs 8 hours x 7 nights = 56 hours for sleep.
Now, let's calculate the time Lisa needs for these activities:
Time for classes + Time for homework + Time for sleep = 8 hours + 21 hours + 56 hours = 85 hours
To find the maximum amount of time Lisa can work, we subtract this total time (85 hours) from the total number of hours in a week (168 hours):
Maximum work hours = Total hours - Total time spent on other activities
Maximum work hours = 168 hours - 85 hours
Therefore, Lisa can work at most 168 hours - 85 hours = 83 hours each week.
The inequality to represent this would be:
x ≤ 83
Where "x" represents the maximum amount of time Lisa can work each week.