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
< > or = to
84 + 89 + 90 = 263 points
400 = total possible points
0.7 * 400 = 280 needed for a C
0.8 * 400 = _____ needed for a B
0.9 * 400 = _____ needed for an A
sorry but I did not, I worked out what you posted and entered them in online and my answers were rejected.
ps. i didn't realize I could respond to you on this
You didn't complete the problem.
For a C, 280 points are needed. Since Joe already has 263 points, he only needs 17 points on the last test for a C.
For a B, 320 points are needed.
320 - 263 = 57 needed
For an A -- 360 points are needed.
360 - 263 = ?
ahh now I see it! 17, 57, 97. not sure what I was thinking there. Thanks for your help!
You're very welcome.
To calculate Joe's average grade, we need to add up his scores and divide by the number of exams.
a) To get a C average, Joe's average grade needs to be between 70 and 79 inclusive.
Let's calculate Joe's current average:
(84 + 89 + 90) / 3 = 87.67
To maintain a C average, Joe's overall average should be 70 <= f + 87.67 / 4 <= 79.
To find the minimum score Joe needs on the final exam, we can rearrange the inequality:
70 <= (f + 87.67) / 4 <= 79
Multiply both sides of the inequality by 4 to isolate f:
280 <= f + 87.67 <= 316
Subtract 87.67 from all sides of the inequality:
280 - 87.67 <= f <= 316 - 87.67
192.33 <= f <= 228.33
Therefore, Joe must score between 192.33 and 228.33 on his final exam to maintain a C average.
b) To get a B average, Joe's average grade needs to be between 80 and 89 inclusive.
80 <= (f + 87.67) / 4 <= 89
Multiply both sides by 4:
320 <= f + 87.67 <= 356
Subtract 87.67 from all sides:
320 - 87.67 <= f <= 356 - 87.67
232.33 <= f <= 268.33
Therefore, Joe must score between 232.33 and 268.33 on his final exam to maintain a B average.
c) To get an A average, Joe's average grade needs to be between 90 and 100 inclusive.
90 <= (f + 87.67) / 4 <= 100
Multiply both sides by 4:
360 <= f + 87.67 <= 400
Subtract 87.67 from all sides:
360 - 87.67 <= f <= 400 - 87.67
272.33 <= f <= 312.33
Therefore, Joe must score between 272.33 and 312.33 on his final exam to maintain an A average.