How to Calculate the Final Quiz Score to Achieve a Desired Average
Mathematical problems involving averages can be quite intriguing, especially when they apply to real-life situations like quiz scores. In this article, we will walk through a step-by-step process to determine the score Annie needs in her final quiz to achieve a desired average score of 25. We will explore different methods and algebraic techniques to find the solution.
Introduction to the Problem
Anne is in the midst of taking quizzes and aims to have a 25 on her average score over five quizzes. She has completed the first four quizzes with scores of 22, 27, 28, and 23. We need to calculate the score she needs in the final quiz to achieve her goal of an overall average of 25.
The key here is understanding that the average score (A) over a set of numbers (N) can be found using the formula:
A (Sum of all scores) / (Number of scores)
To achieve an average of 25 over 5 quizzes, the equation would be:
Average (Score1 Score2 Score3 Score4 Score5) / 5 25
Step-by-Step Solution
Method 1: Sum and Difference Approach
Let's denote the score of the final quiz as x.
We know that the sum of the scores for the first four quizzes is:
22 27 28 23 100
Therefore, the total sum needed to achieve an average of 25 over 5 quizzes is:
Total score needed Average score × Number of quizzes 25 × 5 125
To find out what score x is needed, we use the following equation:
Total score of all 5 quizzes - Total score of the 4 quizzes Score of the 5th quiz
125 - 100 x
Solving this, we find:
x 25
Conclusion: Annie needs to score 25 in her final quiz to get an average score of 25 over all five quizzes.
Method 2: Algebraic Equation Approach
We can set up a simple algebraic equation to represent the situation:
(22 27 28 23 x) / 5 25
Multiplying both sides by 5, we get:
22 27 28 23 x 125
Combining the known scores, we find:
100 x 125
Solving for x, we get:
x 125 - 100
x 25
Conclusion: Again, we find that Annie must score 25 in her final quiz to achieve an average of 25.
Alternative Method: Direct Subtraction
This method directly finds the required score for the final quiz by subtracting the sum of the first four quiz scores from the total required sum:
5 × 25 (desired average) - (22 27 28 23) x
125 - 100 x
x 25
Conclusion: Using this method, we confirm that Annie must score 25 in her final quiz to achieve an average score of 25.
Conclusion and Final Thoughts
The process of calculating the score needed in a final quiz to achieve a desired average score is a practical application of basic algebra and arithmetic concepts. Whether using the sum and difference approach, the algebraic equation method, or direct subtraction, the answer remains consistent: Annie needs to score 25 in her final quiz.
Understanding how to apply these mathematical principles can help in various real-world scenarios, from academic settings to business analytics. Whether you're a student or a professional, developing this skill can be invaluable.