Since the number of ushers is directly proportional to the number of spectators, we can set up a ratio to find the number of ushers needed for 1,050 spectators based on the information given.
We know that:
- For 510 spectators, 17 ushers are needed.
We can set up the following proportion:
\[ \frac{17 \text{ ushers}}{510 \text{ spectators}} = \frac{x \text{ ushers}}{1050 \text{ spectators}} \]
Now solve for \( x \):
\[ x = \frac{17 \text{ ushers} \times 1050 \text{ spectators}}{510 \text{ spectators}} \]
Calculating the right-hand side:
\[ x = \frac{17 \times 1050}{510} \]
\[ x = \frac{17850}{510} \]
Calculating \( \frac{17850}{510} \):
\[ x = 35 \]
Thus, if there are 1,050 spectators, 35 ushers are needed.
The answer is: 35 ushers.