+78 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 50% of all its games by the end of the first n weeks. What is n?
Please write your formula!
+129852
Let q be the number of weeks after the 5th week
We have this equation
total wins [ 2 + 2q ]
_________ = __________ = .50
total games [ 15 + 3q ]
Where n is the number of weeks after the 5th week
Multiply both sides by 15 + 3q and we have that
2 + 2q = .50 [15 + 3q ]
2 + 2q = 7.5 + 1.5q subtract 1.5n, 2 from both sides
.5q = 5.5 divide both sides by .5
q = 11
So..it will take 5 + q = n = 5 + 11 = 16 weeks to reach a 50% winning percentage
Proof:
After n = 16 weeks we have 2 + 2(11) = 24 wins
And 15 + 3(11) = 48 games will have been played
So
24 / 48 = .50
