In an election between two candidates, 64% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 12,288 votes which were 64% of the to... In an election between two candidates, 64% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 12,288 votes which were 64% of the total valid votes. Find the total number of votes enrolled in that election.
Understand the Problem
The question is asking to find the total number of votes enrolled in an election where 64% of the voters cast their votes and 4% of those votes were declared invalid. Given that a candidate received 12,288 votes, which constituted 64% of the valid votes, we will derive the total number of votes from these figures.
Answer
The total number of votes enrolled in the election is $20,000$.
Answer for screen readers
The total number of votes enrolled in the election is $20,000$.
Steps to Solve
- Identify valid votes The candidate received 12,288 votes, which represent 64% of the valid votes.
Let the total valid votes be denoted as $V$:
$$ 0.64V = 12288 $$
To find $V$, we rearrange:
$$ V = \frac{12288}{0.64} $$
- Calculate total valid votes Now, calculate $V$:
$$ V = \frac{12288}{0.64} = 19200 $$
- Determine total votes cast Since 4% of the votes were declared invalid, this means 96% were valid. Let $T$ represent the total votes cast:
$$ 0.96T = V $$
Substituting for $V$:
$$ 0.96T = 19200 $$
- Find total votes enrolled Now, solve for $T$:
$$ T = \frac{19200}{0.96} $$
Calculate:
$$ T = 20000 $$
- Restate total votes Given the equations and calculations, the total number of votes enrolled in the election is 20,000.
The total number of votes enrolled in the election is $20,000$.
More Information
This result means that out of 20,000 enrolled voters, 64% participated in the vote, while 4% of those votes were invalid. The calculations show the relationship between total enrolled votes, valid votes, and the percentage participation and validity.
Tips
- A common mistake is misinterpreting the percentages, particularly not distinguishing between total votes cast and valid votes.
- Failing to adjust the calculations when moving between percentages can lead to incorrect totals.
AI-generated content may contain errors. Please verify critical information
