SOLUTION: a student's grade in a course is determined by 4 quizzes and 1 exam. If the exam counts twice as much as each of the quizzes, what fraction of the final grade is determined by the

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Question 588187: a student's grade in a course is determined by 4 quizzes and 1 exam. If the exam counts twice as much as each of the quizzes, what fraction of the final grade is determined by the exam
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
One way of looking at it is pretending the first 2 quizzes were really one exam and the last 2 quizzes were really another exam. That would be 3 exams worth the same fraction of the grade, so each would be worth 1/3 of the grade.

We can make it look a little more complicated, or a lot more complicated, but I will only go for a little.
If each quiz is worth x as a fraction of the grade, the final is worth 2x as a fraction of the grade.
Adding all the fractions of the grade we get 1%2F1 of the grade (as a fraction).
4%2Ax%2B2x=6x=1 --> x=1%2F6 --> 2x=2%2F6 --> 2x=1%2F3
The exam is worth 1/3 of the grade.

You could also have calculate what fraction of 6x is 2x as
2x%2F6x=%282%2F6%29%28x%2Fx%29=2%2F6=1%2F3
The exam is worth 1/3 of the grade.