Football league

The 3. football league plays each of the 16 participants with each opponent twice. Every victory gets 3 points, 1 point for a draw, a defeat, or none. After the competition, the team had 47 points and 9 defeats at 8. place. How many times has the team won?

Final Answer:

x =  13

Step-by-step explanation:

$$\begin{gathered} 2(16-1)=x+r+9; \\ 47=3x+r \\ 2\cdot 15=x+(47-3x)+9 \\ 2\cdot 15=x+(47-3\cdot x)+9 \\ 2x=26 \\ x=\frac{26}{2}=13 \\ x=13 \\ r=47-3\cdot x=47-3\cdot 13=8 \end{gathered}$$

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