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 $60/%$ of its games by the end of $n$ weeks. What is $n$?

Question

Marcel Navarro

Mathematics

27 April, 18:28

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 $60/%$ of its games by the end of $n$ weeks. What is $n$?

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Answers (1)

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Cohen Mccullough · Answer 1

At the end of the 10 th week

Step-by-step explanation:

My team plays 3 games and lost all of them (12 $) in the first 4 week

so in 4 weeks my team lost 12 $ and all the games

Then total games in three weeks is 4 * 3 = 12

Total lost 12$ then we have a one dolar bet

In the 5th week my team wins 2$ (two games) and at the end of 5th week record is:

From 15 games my team won 2 games and lost 13 games and from that on, my team always wins 2 games then:

Let call x number of week after the 5th then

2 + 2*x / 15 + x = 0,6 0,6 = 60 %

Solving for x

2 + 2*x = 0,6 * (15 + x)

2 + 2*x = 9 + 0,6 * x

2*x - 0,6*x = 9 - 2

2*x - 0,6*x = 7

1,4*x = 7

x = 7/1,4

x = 5 weks later

Then the answer is 10 weeks