How Many Games Were Tied?
Date: 06/07/99 at 18:21:34 From: laura Subject: How many games were tied? Hi! I'm a seventh grade student in Canada and I just finished writing the Gauss Math Competition in the Canadian Mathematics Competition series. There was one problem I skipped, which is extremely frustrating. Can you please give me some help? Here is the problem: In a softball league, after each team has played every other team 4 times, the total accumulated points are: LIONS 22, TIGERS 19, MOUNTIES 14, ROYALS 12. If each team received 3 points for a win, 1 point for a tie and no points for a loss, what is the total number of tied games? My dad and I have tried to solve it using linear and quadratic equations, but it really doesn't offer an adequate answer. Thanks a lot, Laura
Date: 06/07/99 at 18:56:17 From: Doctor Anthony Subject: Re: How many games were tied? Total points 22 + 19 + 14 + 12 = 67 There are 4 teams, so the number of games is 4 x 3 x 4/2 = 24 games (There are 3 games by each team in each round and there are 4 rounds. But each game is played by 2 teams so we divide by 2.) So if a = number of games which end in a win or a loss, b = number of games which are drawn, then a + b = 24 and so b = 24 - a Also 3a + 2b = 67 (remember that both teams earn one point in a draw) 3a + 48 - 2a = 67 a = 19 So there are 19 games in which one or other team wins and then 5 games which are drawn. Therefore 5 games are tied. - Doctor Anthony, The Math Forum http://mathforum.org/dr.math/
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