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.

Consider what we know: the teams have played at least 70 games and at most 162 games. The Peacocks have played and one a combination of games that average to .664, rounded. Assuming rounding is on the up-at-5 rule, we need only do a search of fractions that round to this, where the denominator runs from 70 to 162. We get a choice!

0.663551    71  /  107
0.663636    73  /  110
0.663717    75  /  113
0.663793    77  /  116
0.663866    79  /  119
0.663934    81  /  122
0.664         83  /  125
0.664063    85  /  128
0.664122    87  /  131
0.664179    89  /  134
0.664234    91  /  137
0.664286    93  /  140
0.664336    95  /  143
0.664384    97  /  146
0.66443      99  /  149
0.664474   101  /  152

In all of these cases, the Peacocks win more games!!

Posted by owl on 2004-11-03 12:15:16