Answer:
- best course grade: 84.25%
- least final grade: 63%
Step-by-step explanation:
You have a course average of 79% that is 75% of your grade, and you want to know ...
- the least final score for a course average of 75%
- the best possible course average.
Weighted average
The course average is computed as the weighed average of the course grade so far and the final grade. The weighs are 75% and 25%, respectively. In formula form, the relation between the final grade (f) and the course average (c) is ...
0.75(79) + 0.25f = c
Solving for f, we have ...
f = 4(c -59.25) = 4c -237
a) Best course grade
Assuming the best final grade is 100, the best course grade is ...
c = 0.25(100) +59.25 = 25 +59.25 = 84.25
The best course grade is 84.25%.
b) Least final grade
For a course grade of 75%, the least final grade necessary is ...
f = 4(75) -237 = 300 -237 = 63
The minimum score on the final for a 75% for the course is 63%.
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Additional comment
Here we have percentages with two different bases. The course grade percentages have a base of the greatest possible number of credits. The weight percentages have a base of the whole course grade. Working with percentages of percentages can be confusing if the base of the percentage is not clear.
We often find it easier to deal with grades expressed as a number 0 to 100, rather than as a percentage. That is what we have done here (except in the final answers). The final answer expresses the course grade as a percentage so as to be consistent with the problem statement.
