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

32 ushers
32 ushers

315 ushers
315 ushers

35 ushers
35 ushers

31,500 ushers
31,500 ushers

1 answer

To determine how many ushers are needed for 1,050 spectators, we first need to establish the relationship between ushers and spectators.

We know that the number of ushers is directly proportional to the number of spectators. This can be expressed as:

\[ U = k \cdot S \]

where:

  • \( U \) is the number of ushers,
  • \( S \) is the number of spectators,
  • \( k \) is the constant of proportionality.

From the information provided:

  • When \( S = 510 \), \( U = 17 \).

We can use this to find \( k \):

\[ 17 = k \cdot 510 \]

Solving for \( k \):

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

Now that we have \( k \), we can find the number of ushers needed for \( S = 1,050 \):

\[ U = k \cdot S = \frac{1}{30} \cdot 1,050 \]

Calculating this gives:

\[ U = \frac{1,050}{30} = 35 \]

Therefore, the number of ushers needed for 1,050 spectators is 35 ushers.