Let \( x \) represent the total number of people attending the game. According to the problem, 94% of the attendees supported the home team. Therefore, we can express this relationship with the equation:
\[ 0.94x = 3290 \]
To find \( x \), we can solve the equation by dividing both sides by 0.94:
\[ x = \frac{3290}{0.94} \]
Now, performing the division:
\[ x \approx \frac{3290}{0.94} \approx 3500 \]
Thus, the total number of people attending the game is:
\[ \boxed{3500} \]
To verify, we can check by calculating 94% of 3500:
\[ 0.94 \times 3500 = 3290 \]
Since this is consistent with the information provided, the total number of attendees is confirmed to be:
\[ \boxed{3500} \]
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