An instructor has graded 25 exam papers submitted by students in a class of 26 students, and the average so far is 71. (The maximum possible score is 100.)
A) To raise the class average by 1 point, the score on the last paper has to be:
71 = S/25 so S = 1775 the present sum of all scores after 25 grades
72 (26) = (1775+x)
1872 = 1775 + x
x = 97
To raise the class average by 1 point, the score on the last paper has to be at least 126.
Just kidding! It's impossible to raise the class average by just one paper. The maximum possible score is 100, so even if the last paper got a perfect score, it wouldn't raise the average by a whole point. Keep dreaming though!
To find the score on the last paper needed to raise the class average by 1 point, we can use the following equation:
(Current Average * Number of Students) + Last Score = New Average * Total Number of Students
Given that the current average is 71, the number of students is 26, and the total number of students is also 26:
(71 * 26) + Last Score = (72 * 26)
1854 + Last Score = 1872
Subtracting 1854 from both sides of the equation:
Last Score = 1872 - 1854
The score on the last paper needs to be 18 in order to raise the class average by 1 point.
To raise the class average by 1 point, we first need to determine the total score of all the exams submitted so far. We know that the average of the 25 exam papers is 71, so the total score of those exams would be 25 multiplied by 71.
Total score = 25 * 71 = 1775
To find the score needed on the last paper, we need to achieve the desired average. If we want to raise the class average by 1 point, we need the new average to be 72.
To calculate the score needed on the last paper, we subtract the total score of the exams already graded from the desired total score of all 26 papers.
Desired total score = 26 * 72 = 1872
Score needed on the last paper = Desired total score - Total score of already graded papers
Score needed on the last paper = 1872 - 1775 = 97
Therefore, the score needed on the last paper to raise the class average by 1 point is 97.