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. Show your work
To determine the maximum amount of time Lisa can work each week, we need to subtract the time spent on homework, classes, and sleep from the total number of hours in one week.
The time spent on homework is 21 hours.
The time spent in class is 4 hours twice a week, so 4*2 = 8 hours.
The time spent sleeping is 8 hours per night, so 8*7 = 56 hours.
Therefore, the total time spent on homework, classes, and sleep is 21 + 8 + 56 = 85 hours.
To determine the maximum amount of time Lisa can work, we subtract 85 from the total number of hours in one week: 168 - 85 = <<168-85=83>>83 hours.
Therefore, Lisa can work a maximum of 83 hours each week.
The inequality representing this situation is:
Work hours ≤ Total hours - (Homework hours + Class hours + Sleep hours)
Let x be the number of work hours.
x ≤ 168 - (21 + 8 + 56)
x ≤ 168 - 85
x ≤ 83
Let's break down Lisa's schedule and find out how many hours she can work each week.
1. She has 168 hours in one week.
2. She spends 21 hours per week on homework.
3. She attends two classes, each lasting 4 hours, on Tuesday and Thursday. So, she spends a total of 4 + 4 = 8 hours per week on classes.
4. She wants to ensure 8 hours of sleep each night, which is a total of 8 * 7 = 56 hours per week.
5. So far, we have accounted for 21 + 8 + 56 = 85 hours.
To find out how many hours she can work each week, we subtract the time she spends on various activities from the total number of hours in a week.
168 - 85 = 83
Therefore, Lisa can work a maximum of 83 hours each week.
Inequality: Let's represent the maximum amount of time she can work as "x". The inequality can be set up as:
x ≤ 83
Where "x" represents the number of hours Lisa can work per week.
To determine the maximum amount of time Lisa can work each week, we need to subtract the time dedicated to homework, classes, and sleep from the total number of hours in a week.
First, let's calculate the amount of time Lisa spends on classes:
2 classes x 4 hours/class = 8 hours per week on classes
Next, let's determine the amount of time Lisa needs for sleep:
8 hours of sleep per night x 7 nights = 56 hours per week for sleep
Then, let's combine the time for homework, classes, and sleep:
21 hours for homework + 8 hours for classes + 56 hours for sleep = 85 hours
Finally, subtract the total time from the total number of hours in a week:
168 hours - 85 hours = 83 hours
Therefore, Lisa can work a maximum of 83 hours each week.
To write and solve an inequality for this problem, we can represent the maximum amount of time she can work as "x". The inequality can be written as:
x ≤ 83
This inequality states that "x" must be less than or equal to 83, representing the maximum number of hours Lisa can work each week.