Solving for the Number of Men Who Received Medals in Exactly Two Sports

Oct 13, 2025 by wbrum.org 57 views

Introduction

In this article, we will delve into a mathematical problem involving the distribution of medals in three sports: football, basketball, and cricket. A college has awarded a total of 38 medals in football, 15 in basketball, and 20 in cricket. These medals were received by a total of 58 men, with some men receiving medals in multiple sports. Our objective is to determine the number of men who received medals in exactly two of the three sports.

Given Information

Total medals awarded: 38 (football) + 15 (basketball) + 20 (cricket) = 73
Total men who received medals: 58
Men who received medals in all three sports: 3

Mathematical Formulation

Let's denote the number of men who received medals in football, basketball, and cricket as F, B, and C, respectively. We are given that:

F = 38
B = 15
C = 20
Total men who received medals: F + B + C - (number of men who received medals in exactly two sports) - 2 * (number of men who received medals in all three sports) = 58

We can simplify the equation as:

F + B + C - (number of men who received medals in exactly two sports) - 2 * 3 = 58

Substituting the given values, we get:

38 + 15 + 20 - (number of men who received medals in exactly two sports) - 6 = 58

Solving for the Number of Men Who Received Medals in Exactly Two Sports

Now, let's solve for the number of men who received medals in exactly two sports:

38 + 15 + 20 - (number of men who received medals in exactly two sports) - 6 = 58

Combine like terms:

73 - (number of men who received medals in exactly two sports) = 58

Subtract 73 from both sides:

-(number of men who received medals in exactly two sports) = -15

Multiply both sides by -1:

(number of men who received medals in exactly two sports) = 15

Conclusion

In conclusion, we have determined that 15 men received medals in exactly two of the three sports: football, basketball, and cricket.

Additional Insights

To further understand the distribution of medals, let's consider the following:

The total number of men who received medals in at least one sport is 58.
The number of men who received medals in all three sports is 3.
The number of men who received medals in exactly two sports is 15.
The number of men who received medals in only one sport can be calculated as: F + B + C - (number of men who received medals in exactly two sports) - 2 * (number of men who received medals in all three sports) = 58

This equation can be used to determine the number of men who received medals in only one sport.

Final Thoughts

Introduction

In our previous article, we delved into a mathematical problem involving the distribution of medals in three sports: football, basketball, and cricket. A college has awarded a total of 38 medals in football, 15 in basketball, and 20 in cricket. These medals were received by a total of 58 men, with some men receiving medals in multiple sports. Our objective was to determine the number of men who received medals in exactly two of the three sports.

Q&A Session

Q: What is the total number of medals awarded in the three sports? A: The total number of medals awarded is 38 (football) + 15 (basketball) + 20 (cricket) = 73.

Q: How many men received medals in all three sports? A: 3 men received medals in all three sports.

Q: What is the total number of men who received medals? A: The total number of men who received medals is 58.

Q: How many men received medals in exactly two of the three sports? A: We determined that 15 men received medals in exactly two of the three sports.

Q: Can you explain the mathematical formulation used to solve this problem? A: Yes, the mathematical formulation used was:

F + B + C - (number of men who received medals in exactly two sports) - 2 * (number of men who received medals in all three sports) = 58

Where F, B, and C represent the number of men who received medals in football, basketball, and cricket, respectively.

Q: How can we determine the number of men who received medals in only one sport? A: We can use the equation:

F + B + C - (number of men who received medals in exactly two sports) - 2 * (number of men who received medals in all three sports) = 58

To determine the number of men who received medals in only one sport.

Q: What are some additional insights that can be gained from this problem? A: Some additional insights that can be gained from this problem include:

The total number of men who received medals in at least one sport is 58.
The number of men who received medals in all three sports is 3.
The number of men who received medals in exactly two sports is 15.
The number of men who received medals in only one sport can be calculated using the equation above.

Conclusion

In conclusion, we have provided a Q&A session to further clarify the mathematical analysis of the medal distribution in three sports. We hope that this article has provided a clear understanding of the problem and its solution.

Additional Resources

For further reading on mathematical analysis and problem-solving, we recommend the following resources:

Final Thoughts

In this article, we have used mathematical techniques to analyze the distribution of medals in three sports. By applying basic algebraic manipulations, we have determined the number of men who received medals in exactly two of the three sports. This problem serves as a great example of how mathematical concepts can be applied to real-world scenarios.