Question

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.

Answer 1

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**.