Question

My street hockey team plays three games each week. My team lost all $9$ games in the first three weeks. Then, my team won two games and lost one game in the fourth week, bringing our record to $2$ wins and $10$ losses. Each week after that, my team won two games and lost one game. My team first wins at least $60\%$ of all its games by the end of the first $n$ weeks (including these first four weeks). What is $n$?

Answer 1

After 4 weeks the record is 2–10 (12 games). For each additional week (m weeks after week 4) the team adds 2 wins and 1 loss, so after n = 4 + m weeks:

wins = 2 + 2m, total games = 12 + 3m.

Require (2 + 2m)/(12 + 3m) ≥ 3/5:
5(2 + 2m) ≥ 3(12 + 3m) → 10 + 10m ≥ 36 + 9m → m ≥ 26.

Thus n = 4 + 26 = 30. Check: 54/90 = 0.6.