Question 144709: On the first of four exams, your grades are 82, 75, 80, and 90. There is still a final exam, and it counts as two grades. You are hoping to earn a B in the course. This will occur if the average of your six exam grades is greater than or equal to 80 and less than 90. What range of grades on the final exam will result in earning a B? Use interval notation to express this range.
Okay this is what I got but I'm not sure if I did it right.
 
((327+2x)/6)*6>=80*6 ((327+2x)/6)*6<90*6
327+2x>=480 327+2x<540
-327 -327 -327 -327
2x>=153 2x<213
(2x)/2>=153/2 (2x)/2<213/2
x>=76.5 x<106.5
[76.5,106.5)
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! Your solution is spot on. However, if you had more details about the scoring of the test, you might be able to adjust your interval somewhat. For instance, if you knew that the maximum score on the final was 100, then you could adjust the upper limit to 100] and resign yourself to the fact that an A isn't in the cards. If you knew that the scoring system never results in fractional parts of points, you could adjust the lower limit to the next higher integer, and the upper limit to the next lower integer. Or perhaps the final will consist of 20 questions, each worth 5 points, and no partial credit given. In this case the lower limit could be written either (75 or [80.
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