To solve this problem, we can set up a system of inequalities. Let's represent the number of hours Randall works at the pizza palace as "x" and the number of hours he works at the car wash as "y." The total amount of money he earns per week can be calculated by multiplying the number of hours worked at each job by the respective hourly rate. Since he cannot work more than 25 hours per week, we have the following inequalities: 9x ≤ 25
12y ≤ 25
To find the total amount of money he earns in 8 weeks, we multiply the weekly earnings by 8: 8(9x) + 8(12y) ≥ 1080 Simplifying the equation, we get: 72x + 96y ≥ 1080 Now we have a system of inequalities: 9x ≤ 25
12y ≤ 25
72x + 96y ≥ 1080
To graph the solution region, we can plot the lines for each inequality and shade the region where all the inequalities are satisfied. b. Let's find an example of the number of hours Randall needs to work at each job if he wants to make the trip. We can start by assuming Randall works the maximum number of hours allowed per week, which is 25 hours. For the pizza palace job, since he earns $9 per hour, his weekly earnings would be 9 * 25 = $225. For the car wash job, since he earns $12 per hour, his weekly earnings would be 12 * 25 = $300. Adding up his weekly earnings, Randall would earn $225 + $300 = $525 per week.To find out how many weeks it would take for Randall to save at least $1080, we can divide $1080 by $525: $1080 ÷ $525 ≈ 2.06 weeks Since we can't have a fraction of a week, we can round up to the next whole number. Therefore, Randall would need to work at least 3 weeks to make the trip, working the maximum of 25 hours per week at both jobs. Note: This example assumes Randall only works at the pizza palace and car wash jobs, and doesn't consider any other sources of income or expenses he may have.