Subject: Problem Solving Inequalities Name: Patricia Who are you: Student Your quiz grades are 73, 75, 89 and 91. What is the lowest grade you can obtain on the last quiz and still achieve an average at least 85? Thank you. Hi Patricia, If you had all 5 grades and the average was 85 then the sum of the 5 grades divided by 5 would be 85. Thus the sum of the 5 grades would be 5 85. Penny Hi Patricia. I'll show you how to do this with different numbers: Let's say your quiz grades are 75, 85, 95 and want to achieve an 80 average overall. What minimum score do you need on the fourth and final quiz? Let x be the score of the final quiz. Then the average for the four quizzes is: (75 + 85 + 95 + x ) / 4 and we want a minimum average of 80, so: (75 + 85 + 95 + x ) / 4 ≥ 80 Solve for x: (75 + 85 + 95 + x ) ≥ 80 4 x ≥ 80 4 - 75 - 85 - 95 x ≥ 65 So for this question, you would need at least a 64 on the final quiz to achieve an overall average of 80. Use this method to solve your own question. Stephen La Rocque.