Our badminton team has finished 75% of its season. So far, we have won 20% 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?

Answer 1

Let's start by figuring out how many games we have played so far and how many we have left. If we have finished 75% of the season, that means we have 25% of the season left. If we assume the season is 100 games long, then we have played 75 games and have 25 games left to play.

Next, let's determine how many games we have won so far. If we have won 20% of the games we played, that means we have won 0.2 x 75 = 15 games.

In order to finish the season with the same number of wins as losses, we need to win a total of 37.5 games (half of the 75 games we will have played by the end of the season).

Since we have already won 15 games, we need to win an additional 22.5 games.

To determine what percent of the remaining games we need to win, we can set up the following equation:

(22.5 / 25) x 100% = 90%

So we need to win 90% of the remaining 25 games in order to finish the season with the same number of wins as losses.

Answer 2

Suppose the whole season has g games. At the end of the season, we must have 0.5g wins. The first games during the first 75% of the season has 0.75g games. Since 45% of these are wins, we won 0.45(0.75g) = 0.3375g games during the first 75% of our season. So, we must win 0.5g-0.3375g = 0.1625g games out of the remaining 0.25g games. So, our win percentage must be 0.1625g/0.25g = 0.65 = 65%.