Final answer:
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.