Question

9. Jazmine tutors for $15 per hour. She also works as a dishwasher at her family's restaurant for $8.50 per hour. Her family needs her to be at the restaurant at least 10 hours per week, but she can't work there more than 15 hours per week. She also does not want to work more than a total of 20 hours each week. She wants to make at least $160 per week.

A. Write a system of inequalities to model this scenario and
B. Jazmine wants to earn as much money as possible next
graph the system.
week. What combination of hours should she spend at each job to do this? Justify your reasoning.
C. Jasmine know that in 1 month, her family will need her to work at the restaurant for 10 hours. If Jazmine can tutor in increments of 30 minutes, what is the least amount of time that she could tutor that week to earn $160

Answer 1

Jazmine's work hours and income can be modeled by a system of inequalities with variables representing her tutoring and restaurant work hours. To maximize her weekly income, Jazmine should split her 20 available hours evenly between both jobs. If required to work 10 hours at the restaurant, she needs at least 5 hours of tutoring to make $160.

Step-by-step explanation:

System of Inequalities for Jazmine's Work Scenario

Let's denote the number of hours Jazmine tutors as t and the hours she works at the restaurant as r. The given scenario can be translated into the following system of inequalities:

10 ≤ r ≤ 15: Jazmine needs to work at least 10 hours but no more than 15 hours at the restaurant.

t ≤ 20 - r: Jazmine does not want to work more than a total of 20 hours a week, so the time spent tutoring plus the time at the restaurant should be at most 20 hours.

15t + 8.5r ≥ 160: Jazmine wants to earn at least $160 per week. She earns $15 per hour tutoring and $8.50 per hour at the restaurant.

Maximizing Income

To maximize income, Jazmine should work as many hours as possible at the higher paying job, which is tutoring. Since she can't work more than 20 hours total and must work at least 10 hours at the restaurant, the most tutoring hours would be 10 (20 total hours minus the 10 restaurant hours), allowing her to maximize her income with the higher tutoring rate.

Minimum Tutoring Time for $160

Assuming Jazmine works exactly 10 hours at the restaurant, she would earn $85 there. To make up the remaining $75 needed to reach $160, she would need to tutor for at least 5 hours ($75 divided by $15 per hour). Since she tutors in 30-minute increments, she can work a minimum of 5 hours of tutoring to achieve her goal of $160 for that week.