A basketball team has 12 more games to play. They have won 25 of the 36 games they have played. How many more games must they play in order to finish with a 0.750 record?

Let X = # of games to win to reach .75 record.

.75 = X/48

36 = X

25 + ? = 36

They will need at least 11 games.

To determine how many more games the basketball team must play to finish with a 0.750 record, we need to figure out their desired number of wins and losses.

A 0.750 record means winning 75% of the games. Since the team has already played 36 games and won 25 of them, we can find their win percentage so far:

Win percentage = (wins / total games) * 100
Win percentage = (25 / 36) * 100
Win percentage ≈ 69.4%

To calculate their desired number of wins, we multiply the total number of games by the desired win percentage:

Desired wins = total games * win percentage
Desired wins = (total games / 100) * 75

Since the team wants to finish with a 0.750 record, they desire to win 75% of their total games.

To determine the number of remaining games, we subtract the games played from the total games:

Remaining games = total games - games played
Remaining games = total games - 36

Now we can set up an equation to solve for the remaining games:

Desired wins = (Remaining games / 100) * 75

Let's plug in the values we know:

(36 + Remaining games) * 0.75 = 25

Now we can solve for Remaining games:

0.75 * Remaining games = 25 - (36 * 0.75)
0.75 * Remaining games = 25 - 27
0.75 * Remaining games = -2
Remaining games = -2 / 0.75
Remaining games ≈ -2.67

Since the number of remaining games cannot be negative, we conclude that the basketball team has already surpassed their desired 0.750 record. Therefore, no more games are needed to achieve it.