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

Answer 1

To find out how many ushers are needed when there are 1,050 spectators, we can set up a proportion based on the given information.

We know that:

• When there are 510 spectators, there are 17 ushers.

We can express this as a ratio:

\[ \frac{17 \text{ ushers}}{510 \text{ spectators}} \]

Now, let \( x \) be the number of ushers needed for 1,050 spectators. The proportion then becomes:

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

Now, we can cross-multiply to solve for \( x \):

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

Calculating \( 17 \times 1050 \):

\[ 17850 = 510x \]

Now, solve for \( x \):

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

So, if there are 1,050 spectators, then 35 ushers are needed.

Therefore, the answer is 35 ushers.