Question

My street hockey team plays three games each week. My team lost all 12 games in the first four weeks. Then, my team won two games and lost one game in the fifth week, bringing our record to 2 wins and 13 losses. Each week after that, my team won two games and lost one game. My team first wins at least 50% of all its games by the end of the first n weeks. What is n?

Answer 1

The street hockey team will first win at least 50% of all its games by the end of the eighth week.

Step-by-step explanation:

To find the value of n when the street hockey team first wins at least 50% of all its games, we need to determine at which point the number of wins exceeds half of the total number of games played. From the information given, we know that the team played 12 games in the first four weeks and lost all of them. In the fifth week, they won 2 games and lost 1 game. Thus, after the fifth week, the team had a total of 2 wins and 13 losses.

Each week after that, the team won 2 games and lost 1 game. So, after the sixth week, they had a total of 4 wins and 14 losses. After the seventh week, they had 6 wins and 15 losses. And so on.

In order to exceed 50% wins, the team needs to have more wins than losses. Therefore, we can calculate the number of weeks required by dividing the total number of losses by 2 and adding 1. This is because for every 3 games played, the team wins 2 and loses 1. So, for every 2 losses, the team plays a total of 6 games. Therefore, the number of weeks required is:

(13 losses / 2) + 1 = 6.5 + 1 = 7.5

Since the number of weeks must be a whole number, we round up to the nearest whole number. Therefore, the team first wins at least 50% of all its games by the end of the eighth week.