The Peytonville Peacocks and the Adenville Aardvarks have each played the same number of games so far this season.
The Peacocks have a .664 average, and the Aardvarks have won 70 games. Which team is ahead?
Note that each team plays 162 games in a season, and that the team's average is the number of games won divided by the number of games played rounded off to three decimal places.
(In reply to Solution Using a Slightly Different Aprproach
by Gordon Steel)
"The only integer between 71 and 162 that when multiplied by 66.4% is an integer is the number 125. Therefore, each team played 125 games."
Gordon, while what you said is true, I donít think that is a complete enough proof. Remember the problem defines the average as "the number of games won divided by the number of games played rounded off to three decimal places." So there could be another number combination (like 71/107 = .664) that satisfies the Peacocks average.
The important thing is that there is no number combination where the Peacocks have LESS than 70 wins. What if we were told the teams play 123 games in a season? Then you couldnít find an integer value for the number of games won and played, but the problem would still be solvable.
Posted by nikki
on 2004-11-03 18:14:47