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)

Question

Responses

32 ushers
32 ushers

35 ushers
35 ushers

31,500 ushers
31,500 ushers

315 ushers

Answer 1

We know that the number of ushers ($U$) is directly proportional to the number of spectators ($S$). This can be expressed as:

$$U=kS$$

where $k$ is the constant of proportionality.

From the information provided, when there are 510 spectators, there are 17 ushers. We can use this to find $k$:

$$17=k\times 510$$

To find $k$, we can solve for it:

$$k=\frac{17}{510}=\frac{1}{30}$$

Now that we have found $k$, we can use it to find the number of ushers needed for 1,050 spectators:

$$U=k\times S=\frac{1}{30}\times 1050$$

Calculating this gives:

$$U=\frac{1050}{30}=35$$

Therefore, the number of ushers needed for 1,050 spectators is 35 ushers.