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Question
In a football championship, 153 matches were played, Every two teams played one match with each other. The number of teams, participating in the championship is ______.
Solution
In a football championship, 153 matches were played, Every two teams played one match with each other. The number of teams, participating in the championship is 18.
Explanation:
Let the number of participating teams be n
Given that every two teams played one match with each other.
∴ Total number of matches played = nC2
So nC2 = 153
⇒ `(n(n - 1))/2` = 153
⇒ n2 – n = 306
⇒ n2 – n – 306 = 0
⇒ n2 – 18n + 17n – 306 = 0
⇒ n(n – 18) + 17(n – 18) = 0
⇒ (n – 18)(n + 17) = 0
⇒ n – 18 = 0 and n + 17 = 0
⇒ n = 18, n ≠ – 17
Hence, the value of the filler is 18.
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