Question

Suppose your final grade in a course is 80% of your current grade plus 20% of your final exam score. Your current grade is an 83, and your goal is to get a final grade of 85 or better. Write an inequality to represent this situation and solve it. What must your minimum score on the final exam be to get a grade of at least 85% for the course?

a) 0.8(83) + 0.2x ≥ 85; x ≥ 88.75
b) 0.8(83) + 0.2x ≤ 85; x ≤ 82.5
c) 0.8(83) + 0.2x ≥ 85; x ≥ 81.25
d) 0.8(83) + 0.2x ≤ 85; x ≤ 89.375

Answer 1

To get a grade of at least 85% for the course, the minimum score on the final exam must be 93. The correct answer is d.

Step-by-step explanation:

To write an inequality representing this situation, we can use the formula: 0.8(current grade) + 0.2(final exam score) ≥ 85.

We can substitute the current grade, 83, into the inequality: 0.8(83) + 0.2(final exam score) ≥ 85.

Simplifying this equation gives us: 66.4 + 0.2(final exam score) ≥ 85.

Subtracting 66.4 from both sides gives us: 0.2(final exam score) ≥ 18.6.

Finally, dividing both sides by 0.2 gives us the minimum score needed on the final exam:

final exam score ≥ 93.

Therefore, the correct answer is x ≥ 93, which corresponds to option d) 0.8(83) + 0.2x ≤ 85; x ≤ 89.375.