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?
Without loss of generality, assume they played 250 games.
Then, they've already played 200 games, and won 48/100 * 200 = 96 games.
They need to win 125 games to have 50% wins, which means they need to win 125 - 96 = 29 more games.
They have 50 more games to play, so they must win 29/50 of their games, or 58%.
To check, take the weighted average of the two values. 48 * 80% + 58 * 20% = 50.
This works, as we needed 50% wins/losses.