If a student achieves an average exam score between 70 and 79, he will earn a grade of C in his algebra course. Suppose he has three exam scores of 78 , 65 , and 82 and that his teacher said the final exam score has twice the weight of the other three exams. What range of scores on the final exam will result in him earning a grade of C?

Between 62,5 and 85

Explanation:

As the final exam has twice the weight of the other three exams, the final exam has a weight of 40% and the other three of 20%.

1 exam = 78*0,2=15,6

2 exam=65*0,2=13

3 exam=82*0,2=16,4

4 exam=x*0,4

From this, if you add up all the scores they have to give a result between 70 and 79 to get a C, so:

15,6+13+16,4+x = 70

45+x = 70

x=25

Then, you know that to get 70: x*0,4=25

x=25/0,4 = 62,5

To get 70 you need a score of 62,5 in the final exam.

Then you repeat the same for 79:

45+x = 79

x = 34

x*0,4=34

x=34/0,4 = 85