Question

Scarlett is working two summer jobs, making $13 per hour landscaping and making $8 per hour clearing tables. In a given week, she can work a maximum of 12 total hours and must earn a minimum of $120. If xx represents the number of hours landscaping and yy represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.

Answer 1

Answer:

The graph in the attached figure

Step-by-step explanation:

Let

x ----> the number of hours landscaping

y ---->   the number of hours clearing tables

we know that

she can work a maximum of 12 total

so

$x+y\leq 12$ ----> inequality A

she must earn a minimum of $120

so

$13x+8y\geq 120$ ----> inequality B

Solve the system of inequalities by graphing

The solution is the triangular shaded area

see the attached figure

Remember that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities (the ordered pair lie in the shaded area of the solution set)

One possible solution is the point (10,1)

The point (10,1) lie in the shaded area

That means

The number of hours landscaping is 10 and the number of hours clearing tables is 1