David has a 76% average on the four quizzes he has taken thus far in history class. He has one more quiz to take before final grades are computed, and the five quizzes will be weighted equally.

Question

What is the minimum score that David needs on the fifth quiz in order to raise his average to 80%?

A.100%

B. 90%

C. 96%

D. 84%

Answer 1

76(4) + X = 80(5) = 400

X = [400-76(4)] = 400- 304 = 96 = grade needed to up final grade to 80

Answer 2

Let S = sum of scores on the first four quizzes. Then, S/4 = 76. So, S = 304

Let x = score on quiz five.

(x + 304) / 5 = 80

x + 304 = 400

x = 96

Answer 3

let x1, x2, x3, and x4 denote the scores of the first four quizzes (these are already taken), and x5 the score on the fifth quiz (the one he hasn't taken yet).

Since his current average is 76%, we know that

(x1+x2+x3+x4)/4 = 76

Multiplying both sides by 4, we see that we must have

(x1+x2+x3+x4) = 304.

Now, compute the average for the five quizzes (we want the average to be an 80%).

(x1+x2+x3+x4+x5)/5 = 80. Multiply both sides by 5:

(x1+x2+x3+x4+x5) = 400.

Now, we know what the sum of the first 4 quiz scores is, so sub that in:

(x1+x2+x3+x4)+x5 = 400,

304+x5 = 400.

Hence, x5 = 96.

Therefore, David must score a 96% on the fifth quiz in order to have an 80% average score