SOLUTION: 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, f

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.

--------------------------------------------------------------------------

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.
RELATED QUESTIONS
My sons math question is: Krishan wants his quiz average to be at least 90 so that he can (answered by vleith)

At the end of quarter 1, Sammy wants to have a 90% average. So far he has scored 88, 98,... (answered by TimothyLamb)

Harold wants to get at least a grade of 85 in his math class. His grade will be the... (answered by Boreal)

At the end of quarter 1, Bryan wants to have a 90% average. His first four test scores... (answered by AlgebraLady88)

Marcus wants to end the semester with at least an 85 test average in his math class. On... (answered by fractalier)

a student has forgotten the following grades on his test: 87,95, 86, and 88. he needs to... (answered by addingup)

Abdol Akhim has just come from a Personal Finance class where he learned that he can... (answered by solver91311,ikleyn)

Mike needs at least a 75% average to pass his math course. The class contains 5 exams... (answered by LinnW)

Mike needs at least a 75% average to pass his math course. The class contains 5 exams... (answered by lwsshak3)