Problem of the Week Archive
College Football Championship – January 11, 2016
Problems & Solutions
The College Football Playoff is a four team single elimination tournament. This year
Clemson, Alabama, Michigan State and Oklahoma were in the playoffs. Clemson
played against Oklahoma and had a 54% chance of winning, and Alabama played
against Michigan State and had a 74% chance of winning. Based on these
percentages, what is the percent chance that Alabama and Clemson would
advance to play each other in the championship? Express your answer to the nearest whole number.
Since Clemson had a 54% chance of winning and Alabama had a 74% chance of winning, the chance they would play each
other in the championship was 0.54 × 0.74 = 0.3996, or approximately 40%.
Alabama and Clemson are playing each other in the National Championship tonight. The table
shows the average points per possession for each team,
Category
Alabama
Clemson
as well as, the average number of possessions per
Points per possession
2.56
2.73
game. Based on this data, which team would be
Possessions per game
13.4
14.1
expected to win the championship game, and by how
many points? Express your answer to the nearest whole
number.
If Alabama and Clemson had the points per possession and possessions per game shown in the table, then Alabama would
score 2.56 points × 13.4 possessions = 34.304 points and Clemson would score 2.73 points × 14.1 possessions =
38.493 points. This would mean that Clemson would win by 38.493 – 34.304 = 4.189 ≈ 4 points.
Some sports analysts have predicted Alabama will win the game. Using the data from the previous
problem, if there are 30 total possessions between the two teams, what is the least number of
possessions Alabama will need in order to win the championship game by 1 point or more?
Express your answer to the nearest whole number.
Let’s set up a system of equations using the variable A for the number of Alabama possessions and the variable C for the
number of Clemson possessions. The total number of possessions in the game will be A + C = 30. Based on the table in the
previous problem, for Alabama to win by 1 point or more then 2.56A – 2.73C ≥ 1. Solving for C in the first equation gives us
C = 30 – A. Plugging this into the second equation yields 2.56A – 2.73(30 – A) ≥ 1 → 5.29A – 81.9 ≥ 1 → 5.29A ≥ 82.9 →
A ≥ 15.67. So Alabama will need at least 16 possessions to win.
Problem of the Week Archive
College Football Championship – January 11, 2016
Problems
The College Football Playoff is a four team single elimination tournament. This year
Clemson, Alabama, Michigan State and Oklahoma were in the playoffs. Clemson
played against Oklahoma and had a 54% chance of winning, and Alabama played
against Michigan State and had a 74% chance of winning. Based on these
percentages, what is the percent chance that Alabama and Clemson would
advance to play each other in the championship? Express your answer to the nearest whole number.
Alabama and Clemson are playing each other in the National Championship tonight. The table
shows the average points per possession for each team,
Category
Alabama
Clemson
as well as, the average number of possessions per
Points per possession
2.56
2.73
game. Based on this data, which team would be
Possessions per game
13.4
14.1
expected to win the championship game, and by how
many points? Express your answer to the nearest whole
number.
Some sports analysts have predicted Alabama will win the game. Using the data from the previous
problem, if there are 30 total possessions between the two teams, what is the least number of
possessions Alabama will need in order to win the championship game by 1 point or more?
Express your answer to the nearest whole number.