Final answer:
To calculate the best course grade your friend can earn, we multiply their current average by 75% and add it to the final exam grade multiplied by 25%. The minimum score your friend would need on the final to earn a 75% for the course is 63.
Step-by-step explanation:
To determine the best course grade your friend can earn, we need to calculate the weighted average of their current grade and the final exam grade. Since the final exam counts for 25% of the course grade, we can multiply the friend's current average by 75% (which is 100% - 25%). Let's assume their current average is 79%. Calculating the weighted average:
Course grade = (Current average * 75%) + (Final exam grade * 25%) = (79 * 0.75) + (Final exam grade * 0.25) = 59.25 + Final exam grade * 0.25
Now, let's calculate the minimum score your friend would need on the final to earn a 75% for the course. We want the final grade to be 75%, so setting the equation equal to 75:
75 = 59.25 + Final exam grade * 0.25
Simplifying the equation:
Final exam grade * 0.25 = 75 - 59.25
Final exam grade * 0.25 = 15.75
Dividing by 0.25 on both sides:
Final exam grade = 15.75 / 0.25
Final exam grade = 63