Question

This is for AICE Critical Thinking

There are 12 teams in the Jayhook Hockey League.


Each team plays every other team twice per season, once at home and once away from home.

Last season 34 of the matches played resulted in a tie. Of the others, 18 more were won by the home

team than by the away team.




1: How many games did any one particular team play?


2: How many total games were played in the league?


3: What was the Won-Loss record by Home Teams last season?

Answer 1

Answer:

22 games

132 games

58 - 40

Explanation:

Given that:

Total Number of teams = 12

Number of times a team play every other = 2 (home and away)

Number of ties = 34

Let :

home wins = x

Away wins = x - 18

1: How many games did any one particular team play?

(Total Number of teams - 1) * number of times a team play every other

(12 - 1) * 2

11 * 2 = 22 games

2: How many total games were played in the league?

(Number of games played per team * number of teams) / 2

(22 * 12) / 2

= 264 /2

= 132 games

3: What was the Won-Loss record by Home Teams last season?

Total number of games = 132

Home wins + away wins + ties = 132

x + x - 18 + 34 = 132

2x + 16 = 132

2x = 132 - 16

2x = 116

x = 58

Home team wins = 58

Away team wins = home team loss = 58 - 18 = 40

Hence, Won - Loss record by Home team :

58 : 40