A student's grade in a college course is determined by...

We know that we want the overall weight of the course to be 100%. We have 5 quizzes, 1 midterm, and 1 final. The midterm and the final are each twice the weight of one quiz. So we have the equivalent of 9 quizzes in the course (5 real quizzes, 2 quizzes for the midterm, and 2 quizzes for the final). We can use this information to build an equation for the average overall score in the class.

The student scored an 80 for each of the quizzes. Since there are 5 quizzes, that's a total of 5(80). The student scored a 90 on the midterm. Since the midterm is worth 2 quizzes, that's a total of 2(90). Let's set the students grade on the final as x. Since the final is worth 2 quizzes, that's a total of 2(x).

If we add all of those up, we get everything that goes into the final weight of the class: $$5\left(80\right)+2\left(90\right)+2\left(x\right)$$

Then, to find the average, we can divide by 9, since that's the equivalent number of quizzes that went into this final weight: $$\frac{5\left(80\right)+2\left(90\right)+2\left(x\right)}{9}$$

We want the average final grade of the class to be an 85%, so we can set this equation equal to 85 and then solve for x (the student's grade on the final):
$$\frac{5\left(80\right)+2\left(90\right)+2\left(x\right)}{9}=85$$ $$5\left(80\right)+2\left(90\right)+2\left(x\right)=765$$ $$400+180+2\left(x\right)=765$$ $$580+2\left(x\right)=765$$ $$2\left(x\right)=185$$ $$x=92.5$$

So the student needs a 92.5% on the final to get an average overall grade of 85% in the class.

AAPL wrote:A student's grade in a college course is determined by the scores of 5 quizzes, a midterm exam and a final exam. The midterm exam and the final exam both count twice as much as a quiz in determining the student's average grade. If the student's average a score of 80 on the quizzes and scored a 90 on the midterm exam, then what would the student have to score on the final exam to have an overall average grade of 85 for the entire course?

A. 85.5
B. 90
C. 92.5
D. 93.5
E. 95

We can let x = the student’s grade on the final exam. Since the midterm and final grades count twice, we can create the equation:

[5(80) + 2(90) + 2x]/(5 + 2 + 2) = 85

[400 + 180 + 2x]/9 = 85

580 + 2x = 765

2x = 185

x = 92.5

Answer: C