Kennedy is working two summer jobs, making $16 per hour lifeguarding and making $10 per hour walking dogs. In a given week, she can work a maximum of 13 total hours and must earn no less than $150. Also, she must work at least 8 hours lifeguarding. If x represents the number of hours lifeguarding and y represents the number of hours walking dogs, write and solve a system of inequalities graphically and determine one possible solution.

The answer is below

Explanation:

Let x represent the 9number of hours spent by Kennedy lifeguarding and let y represent the number of hours spent by Kennedy walking dogs.

Given that Kennedy can work a maximum of 13 hours, hence:

x + y ≤ 13                  (1)

Also, she makes $16 per hour lifeguarding and making $10 per hour walking dogs. She must earn no less than $150. Therefore:

16x + 10y ≥ 150         (2)

Lastly, she must work at least 8 hours lifeguarding.

x ≥ 8                          (3)

Also, y > 0

The inequalities are plotted using geogebra online graphing calculator.

We have the following points:

(8, 2.2), (8, 5)

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