Question

Evelyn is working two summer jobs, making $18 per hour tutoring and making $9 per hour landscaping. In a given week, she can work a maximum of 13 total hours and must earn a minimum of $180. If xx represents the number of hours tutoring and yy represents the number of hours landscaping, write and solve a system of inequalities graphically and determine one possible solution.

Answer 1

To solve the problem, define xx as the number of hours tutoring and yy as the number of hours landscaping. Write the inequalities xx + yy ≤ 13 and 18x + 9y ≥ 180. Graph the inequalities and find the region satisfying both. One possible solution is (4, 9).

Step-by-step explanation:

To solve this problem, let's define the variables xx and yy as the number of hours tutoring and landscaping, respectively. The first inequality represents the total number of hours she can work: xx + yy ≤ 13. The second inequality represents the minimum earnings she must make: 18x + 9y ≥ 180. To graph these inequalities, we can plot the points on a coordinate plane and shade the region that satisfies both inequalities. One possible solution is (4, 9), which means Evelyn works 4 hours tutoring and 9 hours landscaping to meet the requirements.