Question

You earn $10 per hour working as a manager at a grocery store. You are required to work at the grocery store at least 8 hours per week. You also teach music lessons for $15 per hour. You need to earn at least $120 per week, but you do not want to wok more than 20 hours per week.

Write a system of linear inequalities that represents the situation. Use x for hours worked at the grocery store and y for hours teaching music lessons.

Answer 1

A system of linear inequalities that represents a student's work hours and earnings with two different jobs is 10x + 15y ≥ 120, x ≥ 8, and x + y ≤ 20, where x is the hours at the grocery store, and y is the hours teaching music.

Step-by-step explanation:

To represent the student's work situation using a system of linear inequalities with x as the hours worked at the grocery store and y as the hours teaching music lessons, we need to consider the following constraints:

The student earns $10 per hour at the grocery store: 10x.

The student earns $15 per hour teaching music lessons: 15y.

The student needs to earn at least $120 per week: 10x + 15y ≥ 120.

The student must work at least 8 hours per week at the grocery store, but not more than 20 hours in total each week: x ≥ 8 and x + y ≤ 20.

The system of linear inequalities that represents this situation is:

10x + 15y ≥ 120

x ≥ 8

x + y ≤ 20

Answer 2

You would have to multiply 120 x 20 then divide by 8. I hope that helps you!