An instructor has graded 23 exam papers submitted by students in a class of 24 students, and the average so far is 73. (The maximum possible score is 100.) How high would the score on the last paper have to be to raise the class average by 1 point?

Let the score be S.

The current total score is
73*23.
The required total score is
74*24
The required score of the last paper is therefore
74*24-73*23
=?

97 However my solution of the problem went a different way than

MathMate. The 24th student would have a base score of 73 and add 24 to it (to raise the average score of all students by 1) would give 97 as the answer.

To determine the score needed on the last paper to raise the class average by 1 point, we can use the following steps:

Step 1: Calculate the current sum of scores
The total sum of scores on the 23 graded exam papers is: 23 * 73.

Step 2: Calculate the current average
To find the current average, divide the sum of scores by the number of graded papers: (23 * 73) / 23.

Step 3: Calculate the current total points
The current total points in the class is equal to the current average multiplied by the total number of students: (23 * 73).

Step 4: Calculate the desired total points
To raise the class average by 1 point, we need to add the desired difference to the current total points: (23 * 73) + 1.

Step 5: Calculate the score needed on the last paper
To find the score needed on the last paper, subtract the current sum of scores from the desired total points: (23 * 73) + 1 - (23 * 73).

By following these steps, the calculated score needed on the last paper to raise the class average by 1 point is 74.

To find out how high the score on the last paper would need to be to raise the class average by 1 point, we can use the following steps:

1. Calculate the total sum of all the grades for the 23 papers that have been graded. We can do this by multiplying the average (73) by the number of graded papers (23): 73 * 23 = 1679.

2. Calculate the sum of all the grades if the average is raised by 1 point. To find this, we add the desired total sum to the sum of the graded papers: 1679 + x (score on the last paper).

3. Calculate the total score if all 24 papers were graded with a maximum score of 100 each. This can be calculated by multiplying the maximum score (100) by the total number of papers (24): 100 * 24 = 2400.

4. Set up an equation using the previous calculations and solve for x (the score on the last paper):
(1679 + x) / 24 = 74, since raising the average by 1 point means it becomes 74.

5. Solve the equation for x by multiplying both sides of the equation by 24 to eliminate the denominator and then subtracting 1679 from both sides:
1679 + x = 74 * 24
x = (74 * 24) - 1679

Calculating this, we find that the score on the last paper would need to be 97 to raise the class average by 1 point.