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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?

 Jul 19, 2022
 #2
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Let the total games    =  12 + 2 + 1 + 3m  =    15 + 3m      where m is the number of weeks after the fifth one

 

And the number of wins  =  2 + 2m

 

So  we wish that

 

[2 + 2m ]  /  [ 15 + 3m ]  =     .50

 

2 + 2m =   .50  [ 15 + 3m ] 

 

2 + 2m =  7.5  + 1.5m

 

2m - 1.5m  = 7.5  - 2

 

.5m    =  5.5

 

m =  5.5  / .5   =    11 weeks  after the 5th one

 

So....you actually  need to play 16 weeks

 

 

cool cool cool

 Jul 19, 2022

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