Suppose that you are taking a course that has three exams which count for three-fifths of your grade and a final which counts for two-fifths of your grade. On your first three tests your scores on were 84, 72, and 96. To get an B in the course, you must have an average of at least 80 percent. What is the minimum score you need on the fourth test to get an B for the course?

Question

Suppose that you are taking a course that has three exams which count for three-fifths of your grade and a final which counts for two-fifths of your grade. On your first three tests your scores on were 84, 72, and 96. To get an B in the course, you must have an average of at least 80 percent. What is the minimum score you need on the fourth test to get an B for the course?

Answer 1

(3/5)(84+72+96)/3 + (2/5)x ≥ 80

times 5
84+72+96 + 2x ≥ 400
2x ≥ 148
x ≥ 74

check:
average of first 3 tests = 84
going towards final mark = (3/5)(84) = 50.4

final mark = 74
(2/5) of that is 29.6
final mark = 50.4 + 29.6 = 80

Answer 2

To calculate the minimum score required on the fourth test to achieve a B in the course, we need to consider the weights of each exam in the final grade.

Given that the three exams count for three-fifths (3/5) of the grade, and the final counts for two-fifths (2/5) of the grade, we can assign weights accordingly.

Let's first calculate the weighted average of the three exam scores:

Weighted Average = (Exam 1 Score * Weight) + (Exam 2 Score * Weight) + (Exam 3 Score * Weight)

Using the given scores:

Weighted Average = (84 * 3/5) + (72 * 3/5) + (96 * 3/5)
Weighted Average = (50.4) + (43.2) + (57.6)
Weighted Average = 151.2

Next, let's calculate the minimum score required on the final exam to achieve an average of at least 80 percent for the entire course:

Total Average = (Weighted Average + Final Exam Score * Weight) / (Total Weight)

Considering an average of at least 80 percent:

80 = (151.2 + Final Exam Score * 2/5) / 1

Now, let's solve the equation to find the minimum score required on the final exam:

80 = (151.2 + Final Exam Score * 2/5)
80 = (151.2/1) + (Final Exam Score * 2/5)
80 - (151.2/1) = Final Exam Score * 2/5
-71.2 = (2/5) * Final Exam Score
Final Exam Score = -71.2 * (5/2)
Final Exam Score = -178

Based on the calculations, it seems that achieving a B grade in the course with the given scores is not possible. It is not mathematically possible to earn a negative score on the final exam. Therefore, further clarification or adjustment of the weights or scores may be required to find a feasible solution.