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.
Let's break down Lisa's time commitments and determine the maximum amount of time she can work each week.
1. Lisa has 168 hours in a week.
2. She sets aside 21 hours for homework.
3. Her two classes each take 4 hours and are once a week on Tuesday and Thursday. So the total time for her classes is 4 hours * 2 classes = 8 hours per week.
4. She wants to ensure 8 hours of sleep each night, which is 8 hours * 7 days = 56 hours per week.
5. So far, Lisa's time commitments are 21 hours for homework + 8 hours for classes + 56 hours for sleep = 85 hours out of 168 available hours.
6. The remaining available hours are 168 hours - 85 hours = 83 hours.
Let's represent the maximum amount of time she can work each week as "x".
The inequality to represent this is:
x ≤ 83 hours
Therefore, Lisa can work at most 83 hours each week.
To determine the maximum amount of time Lisa can work each week, we need to subtract the time she spends on other activities from the total number of hours in one week.
First, let's calculate the total time Lisa spends on homework:
Each class is 4 hours, and she takes two classes, so she spends 4 * 2 = <<4*2=8>>8 hours on classes.
Therefore, she has 21 - 8 = <<21-8=13>>13 hours left for homework.
Next, let's calculate the total time Lisa spends on sleep:
Lisa wants 8 hours of sleep each night, and there are 7 days in a week, so she spends 8 * 7 = <<8*7=56>>56 hours on sleep.
To find the maximum amount of time she can work each week, we can set up an inequality:
Total hours - (hours spent on homework + hours spent on sleep) - hours for classes ≤ hours Lisa can work
The total hours in one week is 168.
Plugging in the values, we get:
168 - (13 + 56) - 8 - 8 ≤ hours Lisa can work
Simplifying the equation:
168 - 13 - 56 - 8 - 8 ≤ hours Lisa can work
168 - 85 ≤ hours Lisa can work
83 ≤ hours Lisa can work
Therefore, Lisa can work at most 83 hours each week.
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.
First, we calculate the total time Lisa spends on classes. Each class is 4 hours long, and she has two classes per week. So the total time spent on classes is 4 hours/class * 2 classes = 8 hours.
Next, we calculate 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 * 7 nights = 56 hours of sleep.
Finally, we add up the time spent on classes and sleep and subtract it from the total number of hours in a week: 168 hours/week - 8 hours (sleep) - 8 hours (classes) = 152 hours.
Now we need to deduct the time Lisa sets aside for homework. She sets aside 21 hours for homework each week. Therefore, she can work at most 152 hours - 21 hours = 131 hours each week.
To write and solve the inequality, let's assign a variable to the amount of time Lisa can work (W). The inequality is:
W ≤ 131
Therefore, the maximum amount of time Lisa can work each week is 131 hours.