A friend has a 82% average before the final exam for a course. That score includes everything but the final, which counts for 30% of the course grade.

What is the best course grade your friend can earn? %

What is the minimum score would your friend would need on the final to earn a 75% for the course? %

So you want to set up an equation for a weighted average. You know the final is 30% of the grade, so everything else is 70%. This gives you:

(Final) (.30) + (other grades) (.70) = course grade

The best grade the student can get would be if they get a hundred on the final, since that's the best score you can make on the final. Then,

(100) (.30) + (82) (.70) = course grade

30 + 57.4 = course grade = 87.4 Which, If you round, the student would get an 87.

For the last part, we use the same equation, just filling in different parts.

(Final) (.30) + (other grades) (.70) = course grade

This time, we don't know the grade for the final, but we know the course grade.

(Final) (.30) + (82) (.70) = 75

(Final) (.30) + 57.4 = 75

(Final) (.30) = 17.6

Final = (17.6) / (.30)

Final = 58.667 Which is approx a 59.