SOLUTION: My street hockey team plays three games each week. My team lost all $9$ games in the first three weeks. Then, my team won one game and lost two games in the fourth week, bringing

Question 1209105: My street hockey team plays three games each week. My team lost all $9$ games in the first three weeks. Then, my team won one game and lost two games in the fourth week, bringing our record to $1$ win and $11$ losses. Each week after that, my team won one game and lost two games. My team first wins at least $60\%$ of all its games by the end of the first $n$ weeks. What is $n$?
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

first three weeks: won 0 games out of 9 games total
through 4 weeks: won 1 game out of 12 games total
through 5 weeks: won 2 games out of 15 games total
through 6 weeks: won 3 games out of 18 games total
...etc...
through n weeks: won n-3 games out of 3n games total

Divide the win count over the total, and multiply by 100, to get the win percentage
For instance if you won A = 3 games out of B = 18 total then winPercentage = (100%)*A/B = (100%)*3/18 = 16.67% approximately

This means 100*(n-3)/(3n) represents the win percentage through the n^th week.

As n gets bigger and bigger, the win percentage will slowly approach 100*n/(3n) = 100*(1/3) = 33.3% approximately. It will never reach this value since this is an asymptote.
So the upper bound is that you'll win a third of your games if you play out to infinity and this pattern of "1 win, 2 losses" continues.
This should be fairly obvious because for any given week you win 1 game out of 3 total.
It's not possible to win 60% of your games no matter how large n gets.

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