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?

Question

answers:

31,500 ushers

35 ushers

32 ushers

315 ushers

Answer 1

To solve the problem, we can use the concept of direct proportionality. The relationship between the number of ushers \( U \) and the number of spectators \( S \) can be expressed as:

\[ U = k \cdot S \]

where \( k \) is the constant of proportionality.

From the information given, when there are 510 spectators, there are 17 ushers. We can use this information to find \( k \):

\[ 17 = k \cdot 510 \]

Now, solving for \( k \):

\[ k = \frac{17}{510} = \frac{1}{30} \]

Now that we have the value of \( k \), we can find out how many ushers are needed when there are 1,050 spectators.

Using the formula:

\[ U = k \cdot S = \frac{1}{30} \cdot 1050 \]

Calculating this gives:

\[ U = \frac{1050}{30} = 35 \]

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

Answer 2

are you sure

Answer 3

Yes, let's verify the calculation step-by-step to ensure we arrive at the correct answer.

1. Understand the proportional relationship: The number of ushers \( U \) is directly proportional to the number of spectators \( S \): \[ U = k \cdot S \]

2. Find the proportionality constant \( k \) using the information given: When \( S = 510 \) spectators, \( U = 17 \) ushers: \[ 17 = k \cdot 510 \] To find \( k \): \[ k = \frac{17}{510} = \frac{1}{30} \]

3. Now calculate the number of ushers for \( S = 1,050 \) spectators: Using the value of \( k \): \[ U = k \cdot S = \frac{1}{30} \cdot 1050 \]

   Performing the calculation: \[ U = \frac{1050}{30} = 35 \]

Thus, the result shows that when there are 1,050 spectators, there are indeed 35 ushers needed.

So yes, I am confident that the answer is correct.