Algebra Homework

Prepared by Matthew S. Sutherland Catching up Name Section Score /100 For the 2014 baseball season in the American league Central division, t he 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 p ts.) MAY 27 th 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 , w hat is Detroit’s average winning percentage? (Write your answer as a fraction . 10 pts. ) 3.) For games 51 through 162 , w hat is K.C. ’s av era ge winning percentage? (Write your answer as a fraction . 10 pts. ) Letting g represent the total number of games played after May 27 th, 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. ) Prepared by Matthew S. Sutherland 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 nu mbers were changed slightly for this example. However, t hey did clinch the wild card and made it to the world series.