Assignment: Catching up
For the 2014 baseball season in the American league Central division, the Detroit Tigers were leading after 50 games played with 30 wins and 20 losses. Kansas City was last after 50 games with only 21 wins and 29 losses*. But, Kansas City catches up.
The winning percentage (PCT) is calculated by dividing the team's total wins by the number of games played.
1.) Calculate the Winning Percentage for each team below:
|
MAY 27th
|
|
|
|
|
AL Central
|
W
|
L
|
PCT
|
|
|
|
|
|
|
Detroit
|
30
|
20
|
|
|
Chicago
|
28
|
27
|
|
|
Minnesota
|
24
|
26
|
|
|
Cleveland
|
24
|
30
|
|
|
K City
|
21
|
29
|
|
For the rest of the season (after game 50), Detroit proceeds to win 15 games for every 13 games lost and Kansas City proceeds to win 17 games for every 11 games lost.
2.) For games 51 through 162, what is Detroit's average winning percentage?
3.) For games 51 through 162, what is K.C.'s average winning percentage?
Letting g represent the total number of games played after May 27th, and w represent the team's total number of wins:
4.) Write an equation that represents Detroit's total wins as a function of g.
5.) Write an equation that represents Kansas City's total wins as a function of g.
6.) Graph each of your equations below on the same graph.
7.) Where do these two graphs intersect?
8.) There are 162 (112 remaining) games in a season. Does Kansas City catch up to Detroit before the season ends?
9.) Fill in the missing data for the final season standings 162 games played.
|
OCT
|
|
|
|
|
AL Central
|
W
|
L
|
PCT
|
|
|
|
|
|
|
Detroit
|
|
|
|
|
K City
|
|
|
|
|
Cleveland
|
85
|
77
|
.525
|
|
Chicago
|
73
|
89
|
.451
|
|
Minnesota
|
70
|
92
|
.432
|
*KC really had 24 wins after the first 50 games. The numbers were changed slightly for this example. However, they did clinch the wild card and made it to the world series.