Question

The number of ushers at a basketball game is directly proportional to the number of spectators. If there are 510 spectators at the game, 17 ushers are needed. How many ushers are needed if there are 1,050 spectators?(1 point)
Responses

31,500 ushers
31,500 ushers

315 ushers
315 ushers

35 ushers
35 ushers

32 ushers

Answer 1

To determine how many ushers are needed for 1,050 spectators given that the number of ushers is directly proportional to the number of spectators, we can set up a proportion based on the initial data provided.

From the information given:
- When there are 510 spectators, there are 17 ushers.

We can express this relationship as:

\[
\frac{\text{Number of ushers}}{\text{Number of spectators}} = k
\]

where \( k \) is a constant of proportionality.

Using the initial numbers:

\[
\frac{17}{510} = k
\]

Calculating \( k \):

\[
k = \frac{17}{510} = \frac{1}{30}
\]

Now, if we want to find the number of ushers (\( U \)) for 1,050 spectators (\( S \)), we set up the equation:

\[
U = k \cdot S
\]

Substituting \( k \) and \( S \):

\[
U = \frac{1}{30} \cdot 1050
\]

Calculating this gives:

\[
U = 35
\]

Thus, if there are 1,050 spectators, 35 ushers are needed.

The correct answer is **35 ushers**.