Two soccer teams are playing inside an arena which can hold up to 3000 fans. As they were arriving, the fans were asked which team they wanted to win. of the fans wanted team A to win the game, and of the fans wanted team B to win. If nobody wanted both teams to win, what is the most number of people that were at the game that did not care which team won?
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We can write our two fractions as 1 4 5 = 7 0 2 5 and 1 5 9 = 7 0 4 2 . So in total 7 0 6 7 of the people were cheering for one team or the other. That means that 7 0 3 of the people were not cheering for any team. Since ⌊ 7 0 3 0 0 0 ⌋ = 4 2 , so at most there were 4 2 × 7 0 = 2 9 4 0 people in the stands, with 7 0 3 × 2 9 4 0 = 1 2 6 of them not cheering for either team.