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'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}.
To determine the maximum amount of time Lisa can work each week, we first need to calculate the total number of hours she has left after accounting for her classes, homework, and sleep.
With two classes that are 4 hours each, twice a week, the total number of class hours per week is 4 hours/class * 2 classes/week = 8 hours/week.
Since she sets aside 21 hours for homework, her total weekly study time is 8 hours (class time) + 21 hours (homework time) = 29 hours.
Considering Lisa wants to ensure 8 hours of sleep each night, her total sleep time per week is 8 hours/night * 7 nights/week = 56 hours/week.
Now, we can subtract Lisa's class and study time and her sleep time from the total number of hours in a week, 168 hours/week, to find out how many hours she has left for work.
Total time available for work = Total hours in a week - Class time - Homework time - Sleep time
Total time available for work = 168 hours - 8 hours - 29 hours - 56 hours = 75 hours.
Therefore, Lisa can work at most 75 hours each week.
To write an inequality to represent this, let w be the maximum number of hours Lisa can work in a week:
w ≤ 75.
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.
First, let's calculate the total number of hours Lisa spends on classes each week. Each class is 4 hours, and she has two classes, so the total class time is 4 hours/class x 2 classes = 8 hours.
Next, let's calculate the time Lisa spends on homework each week. She sets aside 21 hours for homework, so this is already accounted for.
Now, let's consider the time Lisa needs for sleep. She wants to ensure 8 hours of sleep each night, so in a week, she needs 8 hours/night x 7 nights = 56 hours.
Now, let's calculate the time remaining for work. There are 168 hours in a week, and we have already accounted for class time (8 hours) and sleep time (56 hours). Therefore, the remaining time is 168 hours - 8 hours (class time) - 56 hours (sleep time) = 104 hours.
This means that Lisa can work at most 104 hours each week.
To write an inequality to determine the maximum amount of time Lisa can work each week, we can represent the remaining time for work (104 hours) as a variable "w". The inequality would be:
w ≤ 104
So the maximum amount of time Lisa can work each week is 104 hours.