The table shows the final standings of the Quixajuba football championship. In this championship, each team played against each of the other teams four times. Each team earns 3 points for a win, 1 point for a draw, and no points for a loss.

| Team | Points |
| :---: | :---: |
| Bissetriz | 22 |
| Primo | 19 |
| Potência | 14 |
| MDC | 12 |

(a) How many matches were played in the championship?

(b) How many matches ended in a draw?

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(a) There are 6 possible matches between the four teams: (Bissetriz vs Primo), (Bissetriz vs Potência), (Bissetriz vs MDC), (Primo vs Potência), (Primo vs MDC), and (Potência vs MDC). Each of these matches occurred 4 times, so the number of matches is equal to $4 \times 6 = 24$.

(b) The maximum number of points in the championship is 3 times the number of games, that is, $3 \times 24 = 72$. Each time a draw occurs, this number decreases by one unit. Since the total number of points at the end of the championship was $22 + 19 + 14 + 12 = 67$, the number of matches that ended in a draw is $72 - 67 = 5$.