Based on the information given the best course grade your friend can earn is 88.8% the minimum score would your friend would need on the final to earn a 75% for the course is 54%.
Best grade = (84%)(0.7) + (100%)(0.3)
Best grade=0.588+.30
Best grade=0.888 or 88.8%
Let final=30% of the grade
Let class work=(110%-30%)=70%
Let your friend minimum score =f
Hence,
70%(0.84) + 30%(final) = 75%
0.7(0.84) + 0.3f = 0.75
0.588 + 0.3f = 0.75
Collect like terms
0.3f=0.588-0.75
0.3f = 0.162
Divide both side by 0.3f
f=0.162/0.3
f =0.54 or 54%
Inconclusion the best course grade your friend can earn is 88.8% the minimum score would your friend would need on the final to earn a 75% for the course is 54%.
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