Question

Kevin works at two jobs. He mows lawns for $18 per hour and works in a restaurant for $12 per hour. He wants to make at least $300 this week and can work for up to 20 hours. Write and graph a system of inequalities to show the possible combinations of hours that he can work to reach his goal of $300 while working up to 20 hours. List a few possible combinations of hours that he can work.

Answer 1

Kevin needs to solve a system of inequalities to determine how many hours to work at each job to reach his income goal. The inequalities consider his hourly wages ($18 for lawn mowing, $12 for restaurant work), his desire to make at least $300, and his limit of 20 hours of work per week.

Step-by-step explanation:

System of Inequalities for Work Hours and Income

Let's take the number of hours Kevin works mowing lawns as x and the number of hours he works in the restaurant as y. He earns $18 per hour mowing lawns and $12 per hour at the restaurant. Kevin wants to make at least $300, so we can represent this with the inequality 18x + 12y ≥ 300. Since he can work up to 20 hours a week, this gives us two more inequalities: x ≥ 0, y ≥ 0, and x + y ≤ 20. Graphing these inequalities gives us a region showing all possible combinations of hours Kevin can work to meet his goal.

Possible combinations can include, for example, 10 hours of lawn mowing and 5 hours in the restaurant (total earning of $180 + $60 = $240), or 15 hours of lawn mowing and 5 hours in the restaurant (total earning of $270 + $60 = $330). However, since Kevin wants to make at least $300, he would need to work at least 16 ⅓ hours at lawn mowing (since 300 / 18 = 16 ⅓) if he doesn't work at the restaurant at all, or for instance, he can work 8 hours at the restaurant and around 13 hours mowing lawns (8*12 + 13*18 = $96 + $234 = $330).