You have two part-time jobs: in the library paying $7 per hour and at the student radio station paying $9 per hour. You want to earn at least $175 per week. In addition you can only work at most 25 hours per week. Let b be the hours you work in the library each week and let r be the hours that you work at the radio station each week. Is in the solution set of this system of inequalities?

Question

You have two part-time jobs: in the library paying $7 per hour and at the student radio station paying $9 per hour. You want to earn at least $175 per week. In addition you can only work at most 25 hours per week. Let b be the hours you work in the library each week and let r be the hours that you work at the radio station each week. Is  in the solution set of this system of inequalities?

Quizplus · Accepted Answer

Let's set up the system of inequalities to represent the given information:

b + r ≤ 25 (can only work at most 25 hours per week)
7b + 9r ≥ 175 (want to earn at least $175 per week)

To check if 11ec19db_84d0_2b57_9dbe_29178ba48186_TBX8673_11 is in the solution set, we need to substitute b = 11 and r = 11 into the system and see if both inequalities hold true:

11 + 11 ≤ 25 (true)
7(11) + 9(11) ≥ 175 (true)

Since both inequalities are true when b = 11 and r = 11, 11ec19db_84d0_2b57_9dbe_29178ba48186_TBX8673_11 is in the solution set. Therefore, the answer is A.

You Have Two Part-Time Jobs: in the Library Paying $7