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 \(65\%\) of all its games by the end of the first n weeks.  What is n?

 May 14, 2022

We have the inequality: \({2w \over 12 + w} \le {13 \over 20}\), where \(w\) represents the amount of weeks that have gone by (excluding the original 4)


Cross multiplying, we get: \(40 w \le 156 + 13w\).


Now, we have to solve for \(w\) and add 4 to the remaining result. 


Can you take it from here?

 May 14, 2022

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