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.

1 answer

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}.