Dexter And Tommy Took The Same Test.- Dexter Scored 65% On The Test.- Tommy Scored 24 Out Of 40 Marks.Who Got The Higher Score? Justify Your Answer.

Mar 11, 2025 by ADMIN 149 views

**Comparing Scores: A Mathematical Analysis**

Understanding the Problem

In this article, we will delve into a simple yet intriguing problem that involves comparing the scores of two individuals, Dexter and Tommy, who took the same test. We will analyze the given information and determine who scored higher, justifying our answer with mathematical reasoning.

Given Information

Dexter scored 65% on the test.
Tommy scored 24 out of 40 marks.

Calculating Dexter's Score

To compare the scores of Dexter and Tommy, we need to calculate Dexter's score in terms of the total marks. Since Dexter scored 65% on the test, we can calculate his score as follows:

Total marks = 100
Percentage score = 65%
Dexter's score = (65/100) × 100 = 65 marks

Comparing Scores

Now that we have calculated Dexter's score, we can compare it with Tommy's score. Tommy scored 24 out of 40 marks. To compare the scores, we need to calculate Tommy's percentage score:

Tommy's score = 24 marks
Total marks = 40
Percentage score = (24/40) × 100 = 60%

Who Got the Higher Score?

Based on the calculations above, we can see that Dexter scored 65 marks, while Tommy scored 24 marks out of 40. However, when we calculate Tommy's percentage score, we get 60%. Since 65 is greater than 60, Dexter scored higher than Tommy.

Justification

To justify our answer, we can use the concept of equivalent ratios. Since both Dexter and Tommy scored a certain percentage of the total marks, we can set up equivalent ratios to compare their scores:

Dexter's score: 65/100 = x/100 (where x is the total marks)
Tommy's score: 24/40 = y/100 (where y is the total marks)

By cross-multiplying, we get:

65 × 100 = 24 × 100
6500 = 2400

Since 6500 is greater than 2400, we can conclude that Dexter scored higher than Tommy.

Conclusion

In conclusion, Dexter scored higher than Tommy on the test. This is because Dexter scored 65 marks, while Tommy scored 24 marks out of 40. When we calculate Tommy's percentage score, we get 60%, which is lower than Dexter's score of 65. Therefore, we can confidently say that Dexter scored higher than Tommy.

Real-World Applications

This problem may seem simple, but it has real-world applications in various fields, such as:

Education: Comparing scores is an essential aspect of education, where teachers and administrators need to evaluate student performance and identify areas of improvement.
Business: In business, comparing scores is crucial for evaluating employee performance, identifying areas of improvement, and making informed decisions about promotions and bonuses.
Sports: In sports, comparing scores is essential for evaluating team and player performance, identifying areas of improvement, and making informed decisions about strategy and tactics.

Final Thoughts

Q: What if the test had a different total mark? Would the results be the same?

A: Yes, the results would be the same. The percentage score is a ratio of the score to the total marks, so as long as the percentage score is the same, the results would be the same.

Q: How can I calculate the percentage score if I only know the score and the total marks?

A: To calculate the percentage score, you can use the following formula:

Percentage score = (Score / Total marks) × 100

Q: What if I want to compare the scores of two people who took different tests? Can I still use the percentage score?

A: Yes, you can still use the percentage score to compare the scores of two people who took different tests. However, you need to make sure that the tests are of the same difficulty level and that the scoring system is the same.

Q: How can I determine if two people have the same score?

A: To determine if two people have the same score, you can compare their percentage scores. If the percentage scores are the same, then the scores are the same.

Q: What if I want to compare the scores of two people who took the same test, but the test had different sections? Can I still use the percentage score?

A: Yes, you can still use the percentage score to compare the scores of two people who took the same test, but the test had different sections. However, you need to make sure that the sections are of the same difficulty level and that the scoring system is the same.

Q: How can I calculate the average score of a group of people?

A: To calculate the average score of a group of people, you can add up all the scores and divide by the number of people.

Q: What if I want to compare the scores of two people who took the same test, but the test had different time limits? Can I still use the percentage score?

A: Yes, you can still use the percentage score to compare the scores of two people who took the same test, but the test had different time limits. However, you need to make sure that the time limits are of the same difficulty level and that the scoring system is the same.

Q: How can I determine if a person's score is above or below average?

A: To determine if a person's score is above or below average, you can compare their score to the average score of the group.

Q: What if I want to compare the scores of two people who took different types of tests? Can I still use the percentage score?

A: No, you cannot use the percentage score to compare the scores of two people who took different types of tests. The percentage score is only applicable to tests of the same type and difficulty level.

Conclusion

In conclusion, the percentage score is a useful tool for comparing scores, but it has its limitations. You need to make sure that the tests are of the same difficulty level and that the scoring system is the same before using the percentage score. Additionally, you need to consider the time limits and the types of tests when comparing scores.

Real-World Applications

The percentage score has real-world applications in various fields, such as:

Education: Comparing scores is an essential aspect of education, where teachers and administrators need to evaluate student performance and identify areas of improvement.
Business: In business, comparing scores is crucial for evaluating employee performance, identifying areas of improvement, and making informed decisions about promotions and bonuses.
Sports: In sports, comparing scores is essential for evaluating team and player performance, identifying areas of improvement, and making informed decisions about strategy and tactics.