Mrs. Allen a high school teacht is grading quizzes and tests this weekend she has at most 4 hours or 240 minutes to spend grading and she would like to get at least 60 quizzes and tests graded on average it takes her 3 minutes to grade each quiz and 8 minutes to grade each test

Write one inequality to represent the number of quizzes and tests Mrs. Allen must grade and one inequality to represent the number of minutes it will take her to grade the quizzes and tests.

Mrs. Allen must grade at least 60 quizzes and tests, so the sum of x and y must be greater than or equal to 60.

On average, it takes Mrs. Allen 3 minutes to grade each quiz and 8 minutes to grade each test. So, the total number of minutes it takes her to grade x quizzes is 3x minutes, and the total number of minutes it takes her to grade y tests is 8y minutes. Since she has at most 240 minutes to spend grading, the sum of 3x and 8y must be less than or equal to 240.

The solution set to the system of these linear inequalities represents the numbers of quizzes and tests Mrs. Allen can grade this weekend.

Now, consider each of the coordinate points. In order to be a solution to this system of inequalities, both inequalities must be satisfied by the values of x and y. When x = 55 and y = 9, both inequalities are satisfied. To confirm, substitute these values of x and y into the first inequality.

Now substitute the values into the second inequality.

Therefore, the only point that lies in the solution set is (55,9).