To solve this problem, we can use the concept of direct proportionality. Since the number of ushers \( U \) is directly proportional to the number of spectators \( S \), we can express this relationship with the equation:
\[ U = kS \]
where \( k \) is the constant of proportionality.
From the information given, we know that when there are 510 spectators, 17 ushers are required. We can use this information to find \( k \):
\[ 17 = k \times 510 \]
Solving for \( k \):
\[ k = \frac{17}{510} \]
Now we need to calculate \( U \) when there are 1,050 spectators:
\[ U = k \times 1050 \]
Substituting the value of \( k \):
\[ U = \frac{17}{510} \times 1050 \]
Simplifying this calculation:
\[ U = \frac{17 \times 1050}{510} \]
Calculating \( \frac{1050}{510} \):
\[ \frac{1050}{510} = \frac{105}{51} = \frac{35}{17} \]
Now plug this into the equation:
\[ U = 17 \times \frac{35}{17} = 35 \]
Therefore, the number of ushers needed if there are 1,050 spectators is 35 ushers.
The correct response is:
35 ushers.