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

31,500 ushers
31,500 ushers

32 ushers
32 ushers

35 ushers

1 answer

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 based on the information given.

We know that:

  • For 510 spectators, 17 ushers are needed.

We can set up the following proportion:

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

Now solve for \( x \):

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

Calculating the right-hand side:

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

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

Calculating \( \frac{17850}{510} \):

\[ x = 35 \]

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

The answer is: 35 ushers.