Our badminton team has finished $75\%$ of its season. So far, we have won $32\%$ 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?
1 answer
If the team has finished $75\%$ of its season, then $100\% - 75\% = 25\%$ of the season remains. If $32\%$ of the games played has been won, then the team has lost $100\% - 32\% = 68\%$ of the games they played so far. Since the team has played $75\%$ of the games when it has lost $68\%$ of the games played so far, if $(100\%-75\%)$ percent of the games remain, $(100\%-68\%)$ percent of the remaining games must be won in order to finish with the same number of wins as losses. Therefore, $25\% \cdot \frac{100\%-68\%}{100\%-75\%}=\boxed{40\%}$ of the remainder of the games must be won.