In a football

In a football tournament of eight teams, where each team played each other exactly once, points were awarded as follows: the winner of the match received 3 points, the loser received 0 points, and in the event of a draw, each team received 1 point. At the end of the tournament, the sum of the points earned by all teams was 61. What is the maximum number of points the winner of the tournament could have earned?

Correct answer:

x =  21

Step-by-step explanation:

$$\begin{gathered} a_1=3+0=3 \\ {a}_2=1+1=2 \\ n=8 \\ m=\frac{n\cdot (n-1)}{2}=\frac{8\cdot (8-1)}{2}=28 \\ x=(n-1)\cdot a_1=(8-1)\cdot 3=21 \end{gathered}$$

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