Our basketball team has finished 80% of its season, during which we won 48% of the games we played. What percent of the remainder of our games must we win in order to finish the season with the same number of wins as losses?

 Apr 4, 2021

To finish with the same amount of wins as losses, we need to have $50%$ won and $50%$ lost.


Let's break up this season into 20% chunks. Let's denote the percent of games won in each chunk $c_i$, where $i$ denotes which chunk we are on, 1 through 5.


We know have $\frac{c_1+c_2+c_3+c_4}{4}=48$, and we want to have $\frac{c_1+c_2+c_3+c_4+c_5}{5}=50$


Multiplying the first equation by four, we get $c_1+c_2+c_3+c_4=192$.


Multiplying the second equation by five, we get $c_1+c_2+c_3+c_4+c_5=250$


Substituting in $c_1+c_2+c_3+c_4=192$, we get $192+c_5=250$, so ------->$c_5=58%$<-------(for some reason my \boxed{} isn't rendering)


*Note: All the c_i's were in percent form, so, say, $c_2=28$ means that we won $28%$ of our games in chunk $2$, $20%$ to $40%$ of the season.

 Apr 4, 2021

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