Answer:
- C average: m
- B average: m
- A average: m
Explanation:
You want to find the set of final exam scores Rebecca may get for a given grade average. Her scores so far are 81, 83, 87, and all are equally weighted.
Generic solution
Let m represent the exam score Rebecca must get for a final grade score of g. Then we have ...
(m +81 +83 +87)/4 ≥ g
m ≥ 4g -251 . . . . . . . . . . . multiply by 4 and subtract 251
C average
When g=70, we have ...
m ≥ 4(70) -251 = 29 . . . . . lower limit for C
When g=80, we have ...
m ≥ 4(80) -251 = 69 . . . . . upper limit for C, lower limit for B
For a C average, Rebecca must have 29 ≤ m < 69 on her final exam.
B average
When g=90, we have ...
m ≥ 4(90) -251 = 109 . . . . . upper limit for B, lower limit for A
For a B average, Rebecca must have 69 ≤ m < 109 on her final exam.
A average
For an A average, Rebecca must have 109 ≤ m on her final exam.
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Additional comment
Just as no upper limit is put on the interval for an A grade, no upper limit is put on the interval for the final exam score for an A grade. Some exams offer "extra credit" questions, allowing one to achieve a grade greater than 100. We don't know if that is the case here. Rebecca will need that if she plans to obtain an A grade for the class.