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My basketball team plays three games per week. During the first four weeks, we lost all $12$ of our games. During week $5,$ we won two games and lost one game, bringing us to two wins and $13$ losses for the season so far. Each week after that, we won two games and lost one game. At the end of which week will my team have won at least $60\%$ of its games total for the first time in the season?

 Feb 10, 2020
 #1
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Call the number of additional weeks  after the  first  five   =  W

 

And 15 total games have been played during the first  five weeks  = 13 + 2  =15 

 

The number of total  games  past week 5  =  3W

 

And the number of total wins past week 5  = 2W

 

So.....we want to solve this

 

2  +  2W

________   =   .60              multiply both sides by   13 + 3W

15  + 3W

 

2 + 2W  =  .60 ( 15 + 3W)      simplify

 

2 + 2W  =  9  + 1.8W       subtract 1.8W, 2  from both sides

 

.2W  = 7      divide both sides by .2

 

W  = 35

 

So.... 60%  of the games will  be won after week  (5 + 35)   = 40

 

Check.....after 40 weeks     2 + 2(35)  =  72 games will have been won

And   15 + 3(35)  =  120  games would have been played

So   72 /120    =   .60    = 60%

 

 

cool cool cool

 Feb 10, 2020

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