Question 1011435
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: <font size = 5 color = red>94</font>



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.