Joe has scored 84, 89, and 90 on his first three exams in his math class. If the standard 70,80,90 scale is used for grades and the exams are equally weighted, what must he score on the final exam, f, in order to
a) Get a C average on exams?
f
b) Get a B average on exams?
f
c) Get an A average on exams?
f
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To find out what Joe must score on the final exam to achieve a specific average, we need to determine the desired average and then solve for the unknown final exam score, denoted as 'f'.
a) To get a C average on exams, Joe needs to have an average grade within the range of 70-79. We can calculate the average by adding up the scores of all the exams and dividing it by the number of exams. In this case, Joe has taken three exams, so the average is calculated as follows:
(84 + 89 + 90) / 3 = 263 / 3 ≈ 87.67
To achieve a C average, Joe needs his overall average to be within the range of 70-79. Therefore, the final exam score must be within the range of 70-79. In other words:
70 ≤ f ≤ 79
b) To get a B average on exams, Joe needs to have an average grade within the range of 80-89. Following the same steps as above, we calculate the average:
(84 + 89 + 90) / 3 = 263 / 3 ≈ 87.67
To achieve a B average, Joe needs his overall average to be within the range of 80-89. Therefore, the final exam score must be within the range of 80-89. In other words:
80 ≤ f ≤ 89
c) To get an A average on exams, Joe needs to have an average grade within the range of 90-100. Again, we calculate the average:
(84 + 89 + 90) / 3 = 263 / 3 ≈ 87.67
To achieve an A average, Joe needs his overall average to be within the range of 90-100. Therefore, the final exam score must be within the range of 90-100. In other words:
90 ≤ f ≤ 100
In summary:
a) Joe must score between 70 and 79 on the final exam to get a C average.
b) Joe must score between 80 and 89 on the final exam to get a B average.
c) Joe must score between 90 and 100 on the final exam to get an A average.