Our basketball team has finished $80\%$ of its season, during which we won $40\%$ 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?
.40*.80 = .32
so, .20x = .18
x = .9
so, win 90% of the remaining games.
To determine the percentage of the remainder of games we must win, we first need to find the percentage of games we have already played.
Since we have finished $80\%$ of the season, the percentage of games we have already played is $80\%$.
Next, we need to determine the percentage of games we have already won. Since we have won $40\%$ of the games we played, the percentage of games we have won is $40\%$.
To calculate the number of games we have already lost, we subtract the percentage of games we have won from the percentage of games we have played:
$80\% - 40\% = 40\%$
This means that we have lost $40\%$ of the games we have played so far.
To finish the season with the same number of wins as losses, we need to win an equal percentage of the remainder of games.
Let's call the percentage of games we need to win in the remainder of the season $x\%$. Since winning $x\%$ of the remainder of games will result in the same number of wins as losses, the percentage of games we will have won by the end of the season is $40\% + x\%$.
The percentage of games we will have played by the end of the season is $80\% +$ the percentage of the remainder of games. Therefore, the percentage of games we will have played is $80\% + (100\% - 80\%) = 80\% + 20\% = 100\%$.
Since the percentage of games won must be equal to the percentage of games played, we can set up the following equation:
$40\% + x\% = 100\%$
To solve for $x$, we need to isolate it on one side of the equation. We can do this by subtracting $40\%$ from both sides:
$x\% = 100\% - 40\%$
$x\% = 60\%$
Therefore, we must win $60\%$ of the remainder of our games in order to finish the season with the same number of wins as losses.