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,
$
do not want to work more than 20 hours
but you
per week.
a. Write and graph a system of linear inequalities
that represents the situation.
b. Identify and interpret a solution of the system.
c. Use the graph to determine whether you can work
8 hours at the grocery store and teach 1 hour of
music lessons.

Answer 1

We want to get a system of inequalities that models the given situation.

The solutions are:

a) The system is:

• x ≥ 8
• x*$10 + y*$15 ≥ $120
• x + y ≤ 20.
• y ≥ 0

And the graph can be seen at the end.

b) A solution can be x = 12 and y = 2

c) x = 8 and y = 1 is not a solution.

First, we need to define two variables:

• x = number of hours working as a manager.
• y = number of hours teaching lessons.

a) First, we know that you must at least 8 hours per week in the grocery store, then:

x ≥ 8

We know that you need to earn at least $120 per week, then we have the inequality:

x*$10 + y*$15 ≥ $120

And you don't want to work more than 20 hours per week, this gives:

x + y ≤ 20.

We also add the trivial restriction:

y ≥ 0

Then the system is:

• x ≥ 8
• x*$10 + y*$15 ≥ $120
• x + y ≤ 20.
• y ≥ 0

The graph can be seen at the end.

b) The solution region is the interception of the four shaded regions (is the dark blue part).

A solution in that region can be:

x = 12

y = 2

c) The point x = 8, y = 1 is graphed, you can see that it is outside the solution region, thus, this is not a solution.

If you want to learn more about inequalities, you can read:

https://brainly.com/question/2065712