Answer:
Step-by-step 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 [tex]x[/tex].
There are [tex]x-5[/tex] weeks after the fifth week, so there are [tex]3(x-5)[/tex] wins and [tex]x-5[/tex] losses.
So, cumulatively, at the end of [tex]x[/tex] weeks, the team has won [tex]3(x-5)+3[/tex] matches and lost [tex](x-5)+17[/tex] matches.
Team should win 65% of it's games ⇒ [tex]3(x-5)+3\geq \frac{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[/tex]
So, at the end of [tex]30^{th}[/tex] week, the teem would have won atleast 65% of it's matches.
∴ At the end of [tex]30^{th}[/tex] week, the teem would have won atleast 65% of it's matches
