You have two jobs. Job number 1 pays $5 per hour, and job number two pays $7 per hour. You can work no more than 18 hours each week, but you need to earn at least $85 per week.

Question

You have two jobs. Job number 1 pays $5 per hour, and job number two pays $7 per hour. You can work no more than 18 hours each week, but you need to earn at least $85 per week.

Part A: Write a system of linear inequalities to model the situation.

Answer 1

Let's assume that you work x hours in job number 1 and y hours in job number 2.

The first inequality represents the limit on the total number of hours you can work:

x + y ≤ 18

The second inequality ensures that you earn at least $85 per week:

5x + 7y ≥ 85

These two inequalities together form the system of linear inequalities that models the situation:

x + y ≤ 18
5x + 7y ≥ 85