In Mrs. Sotomayor's class, the final grade is based on 6 quizzes and 2 exams. If each exam counts for 3 times as much as each of the quizzes, what fraction of the final grade is determined by each exam?
If each exam = 3 quizzes, then 2 exams = 6 quizzes.
That should help you.
To determine what fraction of the final grade is determined by each exam, we first need to assign weights to the quizzes and exams.
Let's say each quiz is worth Q points and each exam is worth E points. We are given that each exam counts for three times as much as each quiz. So, we can express the weight of the quizzes as 1Q and the weight of the exams as 3Q.
Since the final grade is based on 6 quizzes and 2 exams, the total weight of the quizzes is 6 times the weight of a single quiz: 6 * 1Q = 6Q. Similarly, the total weight of the exams is 2 times the weight of a single exam: 2 * 3Q = 6Q.
Therefore, the fraction of the final grade determined by each exam is 6Q / (6Q + 6Q) = 6Q / (12Q) = 6/12 = 1/2.
Thus, each exam determines 1/2 or half of the final grade.