Question

Jordan is working two summer jobs, making $6 per hour walking dogs and making $15 per hour clearing

tables. In a given week, he can work a maximum of 11 total hours and must earn at least $120. If a represents
the number of hours walking dogs 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 write the system of inequalities, define the number of hours walking dogs as 'a' and the number of hours clearing tables as 'y'. The inequalities are a + y ≤ 11 and 6a + 15y ≥ 120. Graphically, the feasible region is on or below the line a + y = 11 and above the line 6a + 15y = 120. One possible solution is (3, 8).

Step-by-step explanation:

To write the system of inequalities, we first need to define the number of hours Jordan spends walking dogs as 'a' and the number of hours clearing tables as 'y'.

Since Jordan can work a maximum of 11 total hours, we have the inequality a + y ≤ 11.

To ensure that Jordan earns at least $120, we can set up the inequality 6a + 15y ≥ 120.

Graphically, the feasible region will be the area on or below the line a + y = 11 and above the line 6a + 15y = 120. One possible solution can be (3, 8), where Jordan works 3 hours walking dogs and 8 hours clearing tables.