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 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 total points earned by all teams was 61. What is the maximum number of points the tournament winner could have earned?

Final 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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