Question 52917
1)the exam scores are:
70 65 85 80 70 
if the mean of the 3 highest scores represents 65% of their grade and the final exam is 35% of their grade,what is the range of grades in order to achieve a C in the course. round your final answers to the nearest whole number.remember the highest possible grade on the final is 100.
:
I assume they mean what is the range of the final exam score to get a C from the given scores.
:
Average the 3 highest scores [85 + 80 + 70]/3 = 78 (rounded)
:
The ratio of the scores given to the exam score = 65/35 = 13/7 ratio
13 scores of 78 + 7 exam scores (a total of 20 scores) would accomplish this.
:
Let x = final exam score:
:           [(13*78) + 7x]/20 = 70        [lowest av to maintain a C]
:                 [1014 + 7x] = 1400      [Multiplied equation by 20]
:                         7x  = 1400 - 1014
:                          x  = 386/7
:                          x  = 55 is the lowest exam score to get a C
:
:
Exam score to get the highest C (79)
:
:           [(13*78) + 7x]/20 = 79        [hightest av to maintain a C]
:                 [1014 + 7x] = 1580      [Multiplied equation by 20]
                          7x  = 1580 - 1014
                           x  = 566/7
                           x  = 81 is the highest exam score to get a C
:
Range of the exam score would be 55 to 81 for a C
:
: 
2)Can this student get an "A" if the highest possible score on the final exam is 100? Assume that the grade ranges are:
A 90 100
B 80 89
C 70 79
D 60 69
:
:
Using the same method:
:           [(13*78) + 7x]/20 = 90        [lowest av to get an A]
:                 [1014 + 7x] = 1800     [Multiplied equation by 20]
                          7x  = 1800 - 1014
                           x  = 786/7
                           x  = 112 which is impossible, so No!