Question

In a certain course, the Professor has two different grading policies, from which he picks the best. The first policy is to put 40% and 60% weights, respectively, on the midterm and final exams. Under the second grading policy, these weights are 50% each. A student has scored 85% on the midterm, and needs to score at least x% on the final to make a B (a total of 82%). What is the value of x?

A. 82
B. 80
C. 79
D. 81
E. 78

Answer 1

The value of x, the minimum score the student must get on the final to achieve a B, is 80%

Step-by-step explanation:

To find the value of x, we need to determine the minimum score the student must get on the final to achieve a B, which is 82%. Let's calculate the final grade for each grading policy:

Grading Policy 1:

Midterm = 85% x 40% = 34

Final = x% x 60% = 0.6x

Total grade = 34 + 0.6x

Grading Policy 2:

Midterm = 85% x 50% = 42.5

Final = x% x 50% = 0.5x

Total grade = 42.5 + 0.5x

We want the final grade to be at least 82, so we set up the inequality:

34 + 0.6x ≥ 82

42.5 + 0.5x ≥ 82

Solving these inequalities, we find x ≥ 80 for grading policy 1, and x ≥ 79 for grading policy 2. The better option is the higher value, so the value of x is 80.