The number of ushers and a basketball game is directly proportional to the number of spectators there are 510 the game 17 ushers are needed. How many ushers are needed if there are 1050 spectators.

If the number of ushers is directly proportional to the number of spectators, we can use the proportionality relationship to find the number of ushers needed for 1050 spectators.

Given:

• 510 spectators require 17 ushers.

We can set up the proportion:

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

Cross-multiplying gives us:

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

Calculating \(17 \times 1050\):

\[ 17 \times 1050 = 17850 \]

Now we have:

\[ 17850 = 510 \times x \]

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

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

Calculating that:

\[ x = 35 \]

Thus, the number of ushers needed for 1050 spectators is 35 ushers.