An intermediate algebra teacher bases final grades on points earned for activities as given in the Graded Classwork table on the left. To determine final grades, the teacher strictly adheres to the point ranges given in the Grade Distribution table on the right.

Suppose Lauren earns all of the homework and vocabulary points, 50 points for daily activities, and 90 points for lab participation and completion.

Let x = points to be earned on exams.

(a) Write three inequalities to find the minimum number of points she needs on exams to earn grades no lower than A, B, and C.

(b) Solve each inequality from part (a) to find the minimum number of points she needs for each grade. What “test average” (as a percent) corresponds to this number of points, given that exams account for 450 possible points?

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Graded Classwork Activity Homework and vocabulary Daily activities (scaled) Lab participation and completion Major exams (3 at 100 points) Final Exam Total points Points Available 45 55 100 300 150 650 Grade Distribution Grade A B C IP* F In Progress Points Required 585-650 520-584 455-519 < 455 and active < 455 and inactive