Question 1011435: Daniel wants to have a 90 average in his math class at the end of the year. He is trying to determine what he needs to get on his final exam, which accounts for 10% of his grade, for this to work. Tests are weighted 50% of the grade, and he currently has a 85 for his test average; quizzes are weighted 15% of his grade, and he currently has a 95 quiz average; homework is weighted 15% of his grade and he currently has a 98 homework average; and projects are weighted 10% of his grade and he currently has a 92 project average.
What is the lowest whole percentage Daniel can make on his final exam for him to end up with a 90 in the class?
A) 91
B) 92
C) 93
D) 94
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Let x = score on final exam
weights:
final exam = 10% = 0.10
tests = 50% = 0.50
quizzes = 15% = 0.15
homework = 15% = 0.15
projects = 10% = 0.10
Scores:
Final Exam = x
tests = 85 (average)
quizzes = 95 (average)
homework = 98 (average)
projects = 92 (average)
Multiply each weight (the decimal form) by the corresponding score
(weight on final exam)*(final exam score) = 0.10*x = 0.10x
(weight on tests)*(tests score average) = 0.50*85 = 42.5
(weight on quizzes)*(average quiz score) = 0.15*95 = 14.25
(weight on homework)*(average hw score) = 0.15*98 = 14.7
(weight on projects)*(average projects score) = 0.10*92 = 9.2
Add up the products:
0.10x+42.5+14.25+14.7+9.2
That simplifies to
0.10x+80.65
This expression (0.10x+80.65) is the final overall score for the class. Let's call this P
We want P to be 90 or larger, so P >= 90
P >= 90
0.10x+80.65 >= 90
0.10x+80.65-80.65 >= 90-80.65
0.10x >= 9.35
0.10x/0.10 >= 9.35/0.10
x >= 93.5
Recall that we let x = score on final exam. So if x >= 93.5, then the final exam score must be 93.5 or larger. If the teacher only allows whole numbers for the score, then you must get 94 or larger.
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To wrap things up
Question: What is the lowest whole percentage Daniel can make on his final exam for him to end up with a 90 in the class?
Answer: 94
Note: we must round up to ensure we clear the hurdle. If we rounded to 93, then that score isn't big enough to get the overall final grade to 90 or above.
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