The average of several exam scores is 80. One make-up exam was given. Included with the other scores, the new average was 84. If the score on the make up exam was 92, how many total exams were given?
Created: 2 years ago |
Updated: 7 months ago
best des
Let's denote the total number of exams taken as "n."
We are given that the average of several exam scores is 80, which means that the sum of these scores is (n - 1) * 80 because we need to exclude the score of the makeup exam.
The average of the scores, including the makeup exam, is 84. So, the sum of all the scores, including the makeup exam, is n * 84.
We are also given that the score on the makeup exam was 92.
Now, we can set up an equation based on the sum of scores:
Sum of scores (including makeup exam) = Sum of scores (excluding makeup exam) + Score on makeup exam
n * 84 = (n - 1) * 80 + 92
Now, let's solve this equation for "n."
84n = 80n - 80 + 92
Subtract 80n from both sides:
4n = 12
Divide by 4:
n = 3
So, there were a total of 3 exams given.
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