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?

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.

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%.

To find the percentage of the remainder of the games that the team must win, we need to analyze the current win-loss ratio and determine what it needs to be to finish with an equal number of wins and losses.

Since the team has finished 75% of its season and has won 20% of the games played so far, this means the team has lost 80% - 20% = 60% of the games played.

To finish the season with an equal number of wins and losses, the team needs to win the same percentage of the remaining games as they have won so far. This percentage can be found by dividing the percentage of games won by the percentage of the season already completed.

So, the team needs to win 20% / 75% = 0.2667 (or approximately 26.67%) of the remaining games in order to finish with the same number of wins as losses.

To solve this problem, we can break it down into steps:

Step 1: Calculate the number of games played so far.
To determine the number of games played so far, we need to know the total number of games in the season. Let's represent the total number of games as "G", and the number of games already played as "P". Since we are given that the team has finished 75% of its season, we can set up the following equation:

P = 75% of G
P = 0.75G

Step 2: Calculate the number of wins so far.
We are told that the team has won 20% of the games played. Since the number of games played is P (as calculated in step 1), the number of wins can be calculated as:

W = 20% of P
W = 0.2P

Step 3: Calculate the number of losses so far.
The number of losses can be calculated by subtracting the number of wins from the number of games played:

L = P - W

Step 4: Calculate the number of remaining games.
The number of remaining games can be calculated by subtracting the number of games played from the total number of games:

Remaining games = G - P

Step 5: Calculate the number of wins needed to finish the season with the same number of wins as losses.
Since we want the team to finish the season with the same number of wins as losses, we need to determine how many more games the team needs to win. Let's represent this number as "X". We can set up the following equation:

L + X = W + X
Simplifying this equation, we find:
L = W

Since L (number of losses) is equal to W (number of wins), we need to win the same number of remaining games as the number of losses so far.

Step 6: Calculate the percentage of the remaining games that must be won.
To calculate the percentage of the remaining games that must be won, we need to divide the number of wins needed (X) by the number of remaining games:

Percentage of remaining games to win = X / Remaining games

Putting it all together, the percentage of the remainder of the games that must be won in order to finish the season with the same number of wins as losses is X divided by the number of remaining games.