Question

Owen is working two summer jobs, making $25 per hour tutoring and making $10

per hour clearing tables. In a given week, he can work no more than 12 total hours
and must earn a minimum of $150. Also, he must work a maximum of 9 hours
tutoring and a maximum of 4 hours clearing tables. If a represents the number of
hours tutoring and y represents the number of hours clearing tables, write and solve
a system of inequalities graphically and determine one possible solution.

Answer 1

To solve this problem, set up a system of inequalities based on the given constraints for Owen's summer job. Graphically solve the system of inequalities to find one possible solution.

Step-by-step explanation:

To solve this problem, we need to set up a system of inequalities based on the given constraints. Let's use a to represent the number of hours tutoring and y to represent the number of hours clearing tables. First, let's set up the inequality for the total number of hours: a + y ≤ 12. This means that Owen can work no more than 12 total hours. Next, let's set up the inequality for the minimum earnings: 25a + 10y ≥ 150. This means that Owen must earn a minimum of $150. We also need to consider the maximum hours for tutoring and clearing tables: a ≤ 9 and y ≤ 4. To graphically solve this system of inequalities, we can plot the feasible region which represents all the valid combinations of a and y. From the graph, we can identify one possible solution that satisfies all the constraints.