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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?

Jul 27, 2022

#1
0

Jul 27, 2022
#2
+1

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   Jul 27, 2022
#3
+1

thank you!

ILikeSushi  Jul 27, 2022