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)
315 ushers
35 ushers
31,500 ushers
32 ushers

1 answer

To find the number of ushers needed based on the number of spectators, we can use the concept of direct proportionality.

We are given that 17 ushers are needed for 510 spectators. We can set up the following proportion:

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

Let \( x \) be the number of ushers needed for 1,050 spectators:

\[ \frac{x}{1050} = \frac{17}{510} \]

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

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

Calculating the right side:

\[ 17 \cdot 1050 = 17850 \]

Now we have:

\[ x \cdot 510 = 17850 \]

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

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

Now, let's simplify that:

\[ x = 35 \]

Therefore, if there are 1,050 spectators, 35 ushers are needed.

The correct answer is 35 ushers.