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jmc

prealgebra senior

Problem

A sports conference has 14 teams in two divisions of 7. How many games are in a complete season for the conference if each team must play every other team in its own division twice and every team in the other division once?
Solution
Each team plays 6 other teams in its division twice, and the 7 teams in the other division once, for a total of games for each team. There are 14 teams total, which gives a preliminary count of games, but we must divide by two because we have counted each game twice (once for one team and once for the other). So the final answer is games.
Final answer
133