Answer:
The best course grade your friend can earn is 0.867 = 86.7%.
The minimum score would your friend would need on the final to earn a 75% for the course is of 0.61 = 61%.
Step-by-step explanation:
This is a weighed average problem, in which we multiply each grade by its weight.
We have that:
In 70% of the course, the friend has a grade of 81%.
In the other 30%, he will have x.
What is the best course grade your friend can earn?
This will happen if he earns 100% = 1 on the final test. So
[tex]G = 0.7*0.81 + 0.3*1 = 0.867[/tex]
The best course grade your friend can earn is 0.867 = 86.7%.
What is the minimum score would your friend would need on the final to earn a 75% for the course?
This is x, when the grade is 0.75. So
[tex]0.75 = 0.7*0.81 + 0.3x[/tex]
[tex]0.3x = 0.75 - 0.7*0.81[/tex]
[tex]x = \frac{(0.75 - 0.7*0.81)}{0.3}[/tex]
[tex]x = 0.61[/tex]
The minimum score would your friend would need on the final to earn a 75% for the course is of 0.61 = 61%.
