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 315 ushers 315 ushers 35 ushers 35 ushers 32 ushers 32 ushers 31,500 ushers

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.

Given:

• 510 spectators require 17 ushers.

We can set up a proportion:

\[ \frac{17 \text{ ushers}}{510 \text{ spectators}} = \frac{x \text{ ushers}}{1050 \text{ spectators}} \]

To find \(x\), cross-multiply and solve:

\[ 17 \times 1050 = 510 \times x \]

Calculating the left side:

\[ 17 \times 1050 = 17850 \]

Now, we have:

\[ 17850 = 510x \]

To solve for \(x\), divide both sides by 510:

\[ x = \frac{17850}{510} = 35 \]

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