Let the total number of games played by your team be \( x \).
According to your information, you won \( \frac{2}{9} \) of your games. Therefore, the number of games you won is:
\[ \text{Games won} = \frac{2}{9} x \]
You also mentioned that you lost 15 more games than you won, so the number of games lost is:
\[ \text{Games lost} = \text{Games won} + 15 = \frac{2}{9} x + 15 \]
The total number of games played is the sum of games won and games lost:
\[ x = \text{Games won} + \text{Games lost} \]
Substituting the expressions for games won and lost into this equation gives:
\[ x = \frac{2}{9} x + \left( \frac{2}{9} x + 15 \right) \]
This simplifies to:
\[ x = \frac{2}{9} x + \frac{2}{9} x + 15 \] \[ x = \frac{4}{9} x + 15 \]
To isolate \( x \), subtract \( \frac{4}{9} x \) from both sides:
\[ x - \frac{4}{9} x = 15 \] \[ \left(1 - \frac{4}{9}\right)x = 15 \] \[ \frac{5}{9} x = 15 \]
Now, multiply both sides by \( \frac{9}{5} \) to solve for \( x \):
\[ x = 15 \cdot \frac{9}{5} \] \[ x = 27 \]
Therefore, the total number of games played this season is \( \boxed{27} \).
To verify:
- Games won: \( \frac{2}{9} \times 27 = 6 \)
- Games lost: \( 6 + 15 = 21 \)
- Total games: \( 6 + 21 = 27 \)
This confirms that our solution is correct!