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 \(40 \%\) of all its games by the end of the first n weeks. What is n?
+2668 wins = \(2 + 2n\)
losses = \(13 + n\)
This means the equation is \({{2 + 2n} \over 13 + n} = 0.4\)
Multiply each side by \(12 + n \):
\(2 + 2n = 5.2 + 0.4n\)
Subtract \(2\) from both sides:
\(2n=3.2+0.4n\)
Subtract \(0.4n\) from both sides:
\(1.6n=3.2\)
Divide each side by \(1.6 \):
\(n=2\)
This means that after \(2\) weeks, they would have won \(40\)% of their games.
