A team has won 60% of the games it has played so far. If the team wins the 15 remaining games in the season, it will have won 80% of the season's games. How many games will the team play over the entire season?

X = # of games so far.

X+15 = Total @ of games played.

Gw = 0.6x + 15 = Total games won.
Gp = X + 15 = Total games played.

Gw/Gp = (0.6x+15) / (X+15) = 0.80.
Cross multiply:
0.8x + 12 = 0.6x + 15
0.8x - 0.6x = 15 - 12
0.2x = 3
X = 15 Games.

Gp = X + 15 = 15 + 15 = 30 Games.

Let the number of played games in the first place be x. Total number of games is therefore x+15. Then 0.6x games were won in the first place. If the extra 15 will be won, then total games won is 0.6x+15=0.8(x+15). Solving this equation. Then solve for x in this equation. The final answer is therefore the value x add 15 (q.e.d)

To determine the number of games the team will play over the entire season, we can follow these steps:

Step 1: Identify the current percentage of games the team has won.
The team has won 60% of the games it has played so far.

Step 2: Determine the number of games played so far.
Let's assume the team has played "x" games so far. Therefore, the team has won 60% of "x" games, which is 0.6x.

Step 3: Calculate the number of games the team has won.
The team has won 0.6x games so far.

Step 4: Determine the number of games remaining in the season.
Given that there are 15 remaining games in the season, the team needs to win these games to achieve a total percentage of 80% for the entire season.

Step 5: Calculate the total number of games the team will play over the entire season.
If the team wins all 15 remaining games, the total number of games won will be (0.6x + 15).

Step 6: Set up an equation based on the total percentage of games won.
To find the number of games played over the entire season, we set up the following equation:

(0.6x + 15) / (x + 15) = 0.8

The numerator ("0.6x + 15") represents the number of games won (if they win the remaining 15 games) plus the games already won. The denominator ("x + 15") represents the total number of games played (including the remaining 15 games).

Step 7: Solve the equation to find the value of "x".
Now, let's solve the equation:

0.6x + 15 = 0.8(x + 15)

0.6x + 15 = 0.8x + 12

0.6x - 0.8x = 12 - 15

-0.2x = -3

x = -3 / -0.2

x = 15

Therefore, the team has played 15 games so far.

Step 8: Calculate the total number of games played over the entire season.
Using the value of "x", we can determine the total number of games played:

Total number of games = x + 15
Total number of games = 15 + 15
Total number of games = 30

Therefore, the team will play 30 games over the entire season.