Question

At the end of Week 5 of my basketball team's season, our record is 3 wins and 17 losses. Each week after that, we win 3 games and lose 1 game. At the end of which week will my team have won at least $65\%$ of its games total for the first time in the season?

Answer 1

30th week

Explanation:

Basketball team wins 3 matches and loses 17 in the first five weeks.

After fifth week, every week the team wins 3 matches and loses 1 match.

Consider the number of weeks as
`x`.

There are
`x-5` weeks after the fifth week, so there are
`3(x-5)` wins and
`x-5` losses.

So, cumulatively, at the end of
`x` weeks, the team has won
`3(x-5)+3` matches and lost
`(x-5)+17` matches.

Team should win 65% of it's games ⇒
`3(x-5)+3\geq (65)/(100)(3(x-5)+3+(x-5)+17) \\20(3x-12)\geq 13(4x)\\60x-240\geq 52x\\8x\geq 240\\x\geq 30`

So, at the end of
`30^(th)` week, the teem would have won atleast 65% of it's matches.

∴ At the end of
`30^(th)` week, the teem would have won atleast 65% of it's matches