In the Eastern Conference of the National Basketball Association (NBA), the Atlantic, Southeast, and Central Divisions have five teams each. During the regular season, each team plays every other team in its own division four times a year, plays six of the teams from the other two divisions four times a year, plays the remaining four teams from the other two divisions three times a year, and plays each team in the Western conference (which has 15 teams) twice. How many games are played by a team in the Eastern Conference during the regular season?

Question

In the Eastern Conference of the National Basketball Association (NBA), the Atlantic, Southeast, and Central Divisions have five teams each. During the regular season, each team plays every other team in its own division four times a year, plays six of the teams from the other two divisions four times a year, plays the remaining four teams from the other two divisions three times a year, and plays each team in the Western conference (which has 15 teams) twice. How many games are played by a team in the Eastern Conference during the regular season?

show your work

Answer 1

First, calculate the number of games played within each division:

5 teams in each division x 4 games against each team in the division = 20 division games

Next, calculate the number of games played against the other divisions:
6 teams from each of the other two divisions x 4 games against each team = 24 games against those teams
4 teams from each of the other two divisions x 3 games against each team = 12 games against those teams

Finally, calculate the number of games played against the Western Conference:
15 teams in the Western Conference x 2 games against each team = 30 games

Adding up all the games:
20 division games + 24 inter-division games + 12 inter-division games + 30 Western Conference games = 86 games

Therefore, a team in the Eastern Conference plays 86 games during the regular season.