For the 2014 baseball season in the American league Central division, the Detroi
ID: 3044965 • Letter: F
Question
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: (10 pts.)
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?
(Write your answer as a fraction. 10 pts.)
3.)For games 51 through 162, what is K.C.’s average winning percentage?
(Write your answer as a fraction. 10 pts.)
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. (10 pts.)
5.)Write an equation that represents Kansas City’s total wins as a function of g. (10 pts.)
6.)Graph each of your equations below on the same graph. (14 pts.)
7.)Where do these two graphs intersect? (12 pts.)
8.)There are 162 (112 remaining) games in a season. Does Kansas City catch up to Detroit before the season ends? (12 pts.)
9.)Fill in the missing data for the final season standings (162 games played. 12 pts.)
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.
MAY 27th
AL Central
W
L
PCT
Detroit
30
20
Chicago
28
27
Minnesota
24
26
Cleveland
24
30
K City
21
29
Explanation / Answer
1)
2)
51 through 162 is 112 games including both. Detroit wins 15 for every 13 games lost. Hence, 15/28*112=60% wins
3)
51 through 162 is 112 games including both. Kansas City wins 17 for every 11 games lost. Hence, 17/28*112=68% wins
4)
60W+52L=112G
5)
68W+44L=112G
8)
No they dont, they are just lagging behind by 1 game win.
9)
MAY 27th AL Central W L PCT Detroit 30 20 60 Chicago 28 27 50.9090909 Minnesota 24 26 48 Cleveland 24 30 44.4444444 K City 21 29 42