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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?

 Sep 24, 2022
 #1
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Draw a table: (or solve algebraically)

Week 5: 2 wins 13 losses

Week 6: 4 wins 14 losses

Week 7: 6 wins 15 losses

Week 8: 8 wins 16 losses

Week 9: 10 wins 17 losses

Week 10: 12 wins 18 losses

...

Week 13: 18 wins 21 losses

Week 14: 20 wins 22 losses

Week 15: 22 wins 23 losses

Week 16: 24 wins 24 losses

 

To solve algebraically:

f(n) = 2n - 8 wins, n + 8 losses 

2n - 8 = n + 8

n = 16

 Sep 26, 2022

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