To receive a C grade, a student must average more than a 77 but less than 85. If Emma received a C in the course and had five grades of 74,83,73,67,and 85 before taking the final exam, what were the possible grades for her final there were 100 points. (Assume all six grades are weighted equally and let x represent the unknown score)
Well, Emma certainly knows how to keep things interesting with her grades! It seems like she has a range of scores to choose from if she wants to maintain her C grade.
To find out the possible grades for her final, we can start by calculating her current average. Adding up all her previous grades (74 + 83 + 73 + 67 + 85) gives us a total of 382. Since there are 5 grades, her current average is 382/5 = 76.4.
To end up with a C grade, her final average must be more than 77 but less than 85. So, we have the following inequality: 77 < (382 + x)/6 < 85, where x represents her final score.
Let's solve the inequality step-by-step:
77 < (382 + x)/6 < 85
Multiply both sides by 6:
462 < 382 + x < 510
Subtract 382 from all sides:
80 < x < 128
So, the possible grades for Emma's final range from 80 to 128. However, since the exam is out of 100 points, we can narrow it down further.
Since she needs a C grade, her final average cannot exceed 85, meaning x must be less than or equal to (85 - 382) * 6 = -1792. Since we can't have a negative score, we can conclude that Emma's final grade must be between 80 and 100.
So, Emma's possible grades for her final exam are between 80 and 100. Good luck, Emma, and may the clown's funny bone be with you!
To find out the possible grades for Emma's final exam, we need to consider the range within which her average can fall while still receiving a C grade.
According to the given conditions, Emma must average more than a 77 but less than 85 to receive a C grade.
Let's calculate Emma's average score based on the given grades before the final exam:
(74 + 83 + 73 + 67 + 85) / 5 = 382 / 5 = 76.4
Emma's current average is 76.4.
To calculate the range within which Emma's average can fall with the final exam score, we can set up the following inequality:
(382 + x) / 6 > 77
Multiplying both sides by 6:
382 + x > 462
Subtracting 382 from both sides:
x > 80
So, the lowest possible score on the final exam for Emma to receive a C grade is 81.
Now, let's calculate the upper limit:
(382 + x) / 6 < 85
Multiplying both sides by 6:
382 + x < 510
Subtracting 382 from both sides:
x < 128
So, the highest possible score on the final exam for Emma to receive a C grade is 127.
Therefore, the possible grades for Emma's final exam, out of 100 points, can range from 81 to 127.
To find the possible grades for Emma's final, we can start by setting up an inequality to represent the range of scores that would result in a C grade.
Emma needs to average more than a 77 but less than 85 for a C grade. Let's consider the lower and upper bounds separately.
Lower bound:
To average more than a 77, Emma's total points from the five grades (74, 83, 73, 67, 85) plus the points from her final exam (x) must be greater than 77 * 6 = 462.
(74 + 83 + 73 + 67 + 85 + x) > 462
Upper bound:
To average less than 85, Emma's total points from the five grades (74, 83, 73, 67, 85) plus the points from her final exam (x) must be less than 85 * 6 = 510.
(74 + 83 + 73 + 67 + 85 + x) < 510
Now we can solve the inequalities individually to find the range of possible grades for Emma's final.
74 + 83 + 73 + 67 + 85 + x > 462
382 + x > 462
x > 462 - 382
x > 80
74 + 83 + 73 + 67 + 85 + x < 510
382 + x < 510
x < 510 - 382
x < 128
Therefore, the possible grades for Emma's final range from 81 to 127 to ensure she receives a C grade.
The sum of her first 5 scores is 382
6*77 = 462
6*85 = 510
So the last score must satisfy
462 < 382+x < 510
80 < x < 128
So, any score above 80 will get her a C grade.