How do you solve this problem?

In the first five math quizzes, Patty had an average score of 8. She got a 7 and a 5 on the next two quizzes. After the eighth quiz, her average stood at 7.5. What was her score on the eighth quiz?

choices:

A. 5

B. 6

C. 6.5

D. 7.5

E. 8

p.s. please dont just tell me the answer. i want to know HOW to solve it...

How do you solve this problem?

well, she got 8 on the first 5. This means you theoretically have a set (8,8,8,8,8). She got a 7 and 5 on the next two, so your set is now (8,8,8,8,8,7,5). Now you have one more score, which we don't know and shall call "x". Her average afterwards is 7.5. So your set is now (8,8,8,8,8,7,5,x) with an average of 7.5

Averages are calculated as the sum of the set divided by the total number of numbers in the set. See below:

(8 + 8 + 8 + 8 + 8 + 7 + 5 + x)/8 = 7.5, and now you just solve for x.

Hope this helps!

How do you solve this problem?

When you multiply the average by the number of quizzes, you get the total score.

Total for the first 5 quizzes = 5(8)=40

Total for the first 7 quizzes = 40+7+5=52

Assume the score on the 8th quiz is x.

(52+x)/8 = average as we divided the total by the number of quizzes.

(52+x)/8=7.5

multiply both sides by 8

(52+x)=(7.5)(8)

52+x=60

x=60-52=8

The score on the 8th quiz is 8.