If the number of ushers is directly proportional to the number of spectators, we can set up the relationship as follows:
Let \( U \) represent the number of ushers, and \( S \) represent the number of spectators. The relationship can be expressed as:
\[ U = kS \]
where \( k \) is the constant of proportionality.
From the information given, 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, to find how many ushers are needed for 1,050 spectators, we can use the same formula:
\[ U = k \times 1050 \]
First, we need to calculate \( k \):
\[ k = \frac{17}{510} = \frac{1}{30} \]
Now, substituting this value of \( k \) back into the equation for \( U \):
\[ U = \frac{1}{30} \times 1050 \]
Calculating \( U \):
\[ U = \frac{1050}{30} = 35 \]
Therefore, the number of ushers needed if there are 1,050 spectators is 35.