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Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple played in a match, is
840
, then the total numbers of persons, who participated in the tournament, is?
840
, then the total numbers of persons, who participated in the tournament, is?
Most Upvoted Answer
Some couples participated in a mixed doubles badminton tournament. If ...
Understanding the Problem
In a mixed doubles badminton tournament, each match consists of two men and two women, with the condition that no couple can play together. Given that 840 matches were played, we need to determine the total number of participants.
Let’s Define the Variables
- Let n be the number of couples.
- Therefore, there are n men and n women, leading to a total of 2n participants.
Calculating Matches
- Each match requires 1 man from the pool of n men and 1 woman from the pool of n women.
- The total combinations for selecting 1 man and 1 woman (without their couple) can be calculated as follows:
- For each man, you can pair him with (n - 1) women (excluding his partner).
- Hence, the total number of matches is given by:
Matches = n * (n - 1)
Setting Up the Equation
- We know that the total number of matches is 840:
n * (n - 1) = 840
Solving the Equation
- Rearranging gives us:
n^2 - n - 840 = 0
- Factoring the quadratic equation, we find:
(n - 29)(n + 28) = 0
- This gives us n = 30 (since n must be positive).
Calculating Total Participants
- The total number of participants is therefore:
Total Participants = 2n = 2 * 30 = 60
Conclusion
- Hence, the total number of persons who participated in the tournament is 60.
In a mixed doubles badminton tournament, each match consists of two men and two women, with the condition that no couple can play together. Given that 840 matches were played, we need to determine the total number of participants.
Let’s Define the Variables
- Let n be the number of couples.
- Therefore, there are n men and n women, leading to a total of 2n participants.
Calculating Matches
- Each match requires 1 man from the pool of n men and 1 woman from the pool of n women.
- The total combinations for selecting 1 man and 1 woman (without their couple) can be calculated as follows:
- For each man, you can pair him with (n - 1) women (excluding his partner).
- Hence, the total number of matches is given by:
Matches = n * (n - 1)
Setting Up the Equation
- We know that the total number of matches is 840:
n * (n - 1) = 840
Solving the Equation
- Rearranging gives us:
n^2 - n - 840 = 0
- Factoring the quadratic equation, we find:
(n - 29)(n + 28) = 0
- This gives us n = 30 (since n must be positive).
Calculating Total Participants
- The total number of participants is therefore:
Total Participants = 2n = 2 * 30 = 60
Conclusion
- Hence, the total number of persons who participated in the tournament is 60.
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Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple played in a match, is 840, then the total numbers of persons, who participated in the tournament, is?
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Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple played in a match, is 840, then the total numbers of persons, who participated in the tournament, is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple played in a match, is 840, then the total numbers of persons, who participated in the tournament, is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple played in a match, is 840, then the total numbers of persons, who participated in the tournament, is?.
Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple played in a match, is 840, then the total numbers of persons, who participated in the tournament, is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple played in a match, is 840, then the total numbers of persons, who participated in the tournament, is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple played in a match, is 840, then the total numbers of persons, who participated in the tournament, is?.
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