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?
+487 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.
