https://file.aiquickdraw.com/mathbot/file/1726278931890aj8w6wzv.jpg

The question in the image is in Hindi, and it translates to:

"In an election, 2105 people did not vote. Out of the total votes cast, 3215 votes were invalid. Candidate A received 47% of the valid votes, while candidate B received 11,400 votes. What was the total number of registered voters?"

Let's break it down:

- 2105 people did not vote.
- 3215 votes were invalid.
- Candidate A received 47% of valid votes.
- Candidate B received 11,400 votes.

We are tasked with finding the total number of registered voters.

### Step-by-step approach:

Let the total number of voters (registered) be denoted by **N**.

1. **Total Votes Cast**:  
   If 2105 people did not vote, then the total number of votes cast = \( N - 2105 \).

2. **Valid Votes**:  
   Out of the votes cast, 3215 votes were invalid. Therefore, the number of valid votes = \( (N - 2105) - 3215 = N - 5320 \).

3. **Votes for Candidate A and B**:  
   Candidate A received 47% of the valid votes, and candidate B received 11,400 votes.  
   So, votes received by candidate A = \( 0.47 \times (N - 5320) \).  
   Since the sum of the votes for both candidates is equal to the total number of valid votes:  
   \[
   0.47 \times (N - 5320) + 11400 = N - 5320
   \]

4. **Solve for N**:  
   Now we can solve this equation to find the total number of registered voters.

Let's calculate.The total number of registered voters is approximately **26,829**.

Do you want more details on the solution or have any questions?

Here are 5 related questions to further explore:

1. How do we calculate the number of valid votes if a percentage of votes is invalid?
2. What happens if Candidate A's percentage of votes changes to 50%? How does it affect the outcome?
3. How can we verify the number of registered voters from the result we obtained?
4. If the number of invalid votes is reduced, how does it impact the final count of registered voters?
5. What mathematical concept is applied to solve equations with percentages like this?

**Tip:** When dealing with percentages in a problem, always ensure you calculate them based on the correct total, whether it’s votes cast or valid votes!

In an election, 2105 people did not vote. Out of the total votes cast, 3215 votes were invalid. Candidate A received 47% of the valid votes, while candidate B received 11,400 votes. What was the total number of registered voters?

Find the total number of registered voters in an election problem where 2105 people didn't vote, 3215 votes were invalid, and candidate A received 47% of the valid votes, while candidate B received 11,400 votes. Suitable for Grades 9-10.

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