Introduction
In this mathematical exploration, we delve into a scenario involving a school with a total student population of 7000. Our focus is to determine the number of students who have a penchant for playing badminton, given that 65% of the student body expresses their fondness for hockey. This problem allows us to apply fundamental percentage concepts and arithmetic operations to arrive at a concrete solution. To accurately determine the number of students who prefer badminton, we must first calculate the percentage of students who do not favor hockey, as they constitute the group inclined towards badminton. This involves subtracting the percentage of hockey enthusiasts from the total percentage (100%). Subsequently, we can apply this derived percentage to the total student population to pinpoint the exact number of badminton-loving students. This exercise not only reinforces our understanding of percentages but also highlights their practical application in real-world scenarios, such as analyzing student preferences within an educational institution. By carefully dissecting the problem and employing logical steps, we can arrive at a precise answer that sheds light on the sporting inclinations of the student body. The following sections will guide you through the detailed calculations and reasoning behind the solution, ensuring a comprehensive understanding of the problem-solving process.
Determining the Percentage of Badminton Players
To accurately calculate the number of students who enjoy playing badminton, our initial step involves determining the percentage of students who do not share the enthusiasm for hockey. We know that 65% of the students are inclined towards hockey, and the entire student population represents 100%. Therefore, we can deduce the percentage of badminton players by subtracting the percentage of hockey players from the total percentage. This is a fundamental concept in percentage calculations, where the whole (100%) is used as the reference point to determine the proportion of different parts. The calculation is straightforward: 100% (total students) - 65% (hockey players) = 35%. This result signifies that 35% of the students in the school prefer badminton over hockey. This percentage is a crucial piece of information, as it directly relates to the number of students we are trying to find. Understanding this percentage allows us to move forward in our calculation, applying it to the total student population to arrive at the specific number of badminton enthusiasts. This step highlights the importance of understanding percentage relationships and how they can be used to solve practical problems. By establishing this percentage, we have laid the groundwork for the final calculation, which will reveal the exact number of students who enjoy badminton. This process demonstrates how a seemingly simple percentage calculation can provide valuable insights into the preferences of a large group, in this case, the student body of the school.
Calculating the Number of Badminton Players
Now that we've established that 35% of the students prefer badminton, we can proceed to calculate the actual number of students this percentage represents. We know the total number of students in the school is 7000. To find 35% of 7000, we convert the percentage into a decimal by dividing it by 100, which gives us 0.35. This decimal representation of the percentage allows us to easily multiply it with the total number of students to find the corresponding number of badminton players. The calculation is as follows: 0.35 (decimal equivalent of 35%) * 7000 (total students) = 2450 students. This result indicates that 2450 students in the school enjoy playing badminton. This calculation demonstrates the practical application of percentages in real-world scenarios, allowing us to determine a specific quantity based on a proportion of a whole. The process of converting a percentage to a decimal and then multiplying it with the total quantity is a fundamental skill in mathematics and is widely used in various fields, including finance, statistics, and everyday problem-solving. By accurately performing this calculation, we have successfully answered the question posed, revealing the number of students who have a preference for badminton. This information could be valuable for the school administration in planning extracurricular activities and allocating resources to cater to the interests of the students.
Solution
Therefore, based on our calculations, the number of students who like to play badminton is 2450. This conclusion is derived from the initial information that 65% of the 7000 students prefer hockey, which implied that the remaining 35% are inclined towards badminton. By converting this percentage into a decimal (0.35) and multiplying it by the total number of students (7000), we arrived at the precise figure of 2450. This solution not only answers the specific question but also showcases the application of mathematical concepts in understanding and analyzing real-world scenarios. The ability to interpret percentages and apply them to calculate specific quantities is a valuable skill that extends beyond the classroom and into various aspects of life. The process of solving this problem reinforces the importance of careful reading, logical deduction, and accurate calculation. By breaking down the problem into smaller steps, we were able to systematically arrive at the solution, demonstrating a clear and concise approach to problem-solving. This approach can be applied to a wide range of mathematical problems and is an essential tool for students and professionals alike.
Conclusion
In conclusion, this exercise has effectively demonstrated how basic mathematical principles, specifically percentages, can be applied to solve practical problems. We successfully determined that 2450 students out of a total of 7000 in the school prefer playing badminton, given that 65% favor hockey. This problem-solving process involved several key steps, including understanding the relationship between percentages and proportions, converting percentages to decimals, and performing accurate multiplication. The ability to solve such problems is crucial for developing analytical skills and applying mathematical knowledge in real-world contexts. Moreover, this exercise highlights the importance of clear and logical reasoning in approaching mathematical challenges. By breaking down the problem into manageable steps, we were able to arrive at a precise and meaningful solution. This approach not only enhances our understanding of the specific problem but also equips us with a valuable problem-solving methodology that can be applied to a wide range of situations. The final answer, 2450 students, provides a clear and concise representation of the number of badminton enthusiasts in the school, offering valuable information for the school administration and potentially influencing decisions related to sports programs and resource allocation. This exercise serves as a reminder of the practical relevance of mathematics and its ability to provide insights into various aspects of our lives.
