Dominic is working two summer jobs, making $10 per hour babysitting and making $6 per hour walking dogs. In a given week, he can work no more than 16 total hours and must earn at least $120. If x represents the number of hours babysitting and y represents the number of hours walking dogs, write and solve a system of inequalities graphically and determine one possible solution.

The graphical solution is given at the end of the answer, and one possible solution is 12 hours babysitting and 3 hours walking the dog.

What is a system of inequalities?

A system of equations is when two or more variables are related, and inequalities are built to find the values of each variable.

For this problem, the variables are given as follows:

Variable x: number of hours babysitting.

Variably y: number of hours walking dogs.

He can work no more than 16 total hours, hence:

x + y ≤ 16.

He must earn at least $120, hence, considering the earnings with each activity:

10x + 6y ≥ 120.

These two inequalities compose the system. The graphical solution is composed by points that:

Are to the left of line y = 16 - x.

Are to the right of line -1.67x + 20.

Above y = 0, as there are no negative times.

The graphical solution is given by the region shaded in blue at the end of the answer.

One possible solution inside the region is:

(12,3).

Meaning that he can work 12 hours babysitting and 3 hours walking the dog.

More can be learned about a system of inequalities at https://brainly.com/question/9774970

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