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.

Answer 1

Lisa's total hours for classes are 4 hours/class x 2 classes = <<4*2=8>>8 hours.
Her classes are on 2 days a week, so her total class time is 8 hours x 2 = <<8*2=16>>16 hours.
Her total hours for sleep are 8 hours/night x 7 nights = <<8*7=56>>56 hours.
Her total time for class and sleep is 56 hours + 16 hours = <<56+16=72>>72 hours.
Lisa sets aside 21 hours for homework and has 72 hours for class and sleep, so she has 168 hours - 21 hours - 72 hours = <<168-21-72=75>>75 hours to spare each week.
To determine the maximum amount of time Lisa can work, we need to subtract the hours she has to spare from the 168 hours in one week. We can represent this as an inequality: 168 - 21 - 72 - x ≥ 0.
By solving the inequality, we have 75 - x ≥ 0.
To solve for x, we subtract 75 from both sides of the inequality: -x ≥ -75.
Then, multiply both sides by -1 to get the value of x: x ≤ 75.
Therefore, Lisa can work at most 75 hours each week. Answer: \boxed{75}.