Let \( x \) be the total number of students surveyed. According to the information given:
- 484 students chose purple.
- 45% of the students chose blue, which can be expressed as \( 0.45x \).
The total number of students who participated can be calculated by adding the number of students who favored purple and those who favored blue:
\[ 484 + 0.45x = x \]
To solve for \( x \), we can first rearrange the equation:
\[ 484 = x - 0.45x \]
This simplifies to:
\[ 484 = 0.55x \]
Now, we can solve for \( x \) by dividing both sides of the equation by \( 0.55 \):
\[ x = \frac{484}{0.55} \]
Calculating the right side:
\[ x = 880 \]
Thus, the total number of students surveyed is \( \boxed{880} \).