A poll of 400 randomly selected likely voters in Seanoa city was taken to determine the support for the mayoral candidates in the upcoming election. Of the likely voters selected,190 stated that they are likely to vote for Candidate A. If the conclusion is drawn that "approximately 3,120 voters are likely to vote for Candidate A", which of the following is closest to the number of likely voters is Seanoa city?

Options

A. 1482
B. 3120
C. 4741
D. 6568

Answer

To solve the problem, we need to find the total number of likely voters in Seanoa city based on the information provided from the poll. Here’s a step-by-step solution:

### Step 1: Understand the Poll Results
From the poll of 400 likely voters:
- 190 stated they are likely to vote for Candidate A.

### Step 2: Set Up the Proportion
We can set up a proportion based on the poll results and the conclusion drawn:
\[ \frac{190}{400} = \frac{3120}{x} \]
Where \( x \) is the total number of likely voters in Seanoa city.

### Step 3: Cross-Multiply to Solve for \( x \)
Cross-multiplying gives us:
\[ 190 \cdot x = 3120 \cdot 400 \]

### Step 4: Calculate the Right Side
Now, calculate \( 3120 \cdot 400 \):
\[ 3120 \cdot 400 = 1248000 \]

### Step 5: Solve for \( x \)
Now, we can substitute back into the equation:
\[ 190x = 1248000 \]
To find \( x \), divide both sides by 190:
\[ x = \frac{1248000}{190} \]

### Step 6: Perform the Division
Now, perform the division:
\[ x = 6568.42 \]

### Step 7: Round to the Nearest Whole Number
Since we are looking for the closest whole number, we round \( 6568.42 \) to \( 6568 \).

### Conclusion
Thus, the closest estimate to the number of likely voters in Seanoa city is **6568**.

---