Election Voter Calculation Steps
This problem requires calculating the total number of registered voters based on the percentage of votes polled, invalid votes, the winner's share of valid votes, and the winning margin.
1. Calculate Valid Votes Percentage
- Let V be the total number of registered voters.
- Percentage of voters who cast votes = 92%.
- Votes Polled = $0.92 \times V$.
- Percentage of invalid votes = 20%.
- Percentage of valid votes = $100\% - 20\% = 80\%$.
- Valid Votes = $80\%$ of Votes Polled = $0.80 \times (0.92 \times V) = 0.736V$.
2. Determine Margin Percentage
- The winning candidate secured 75% of the valid votes.
- This implies the losing candidate received $100\% - 75\% = 25\%$ of the valid votes.
- The margin of victory is the difference: $75\% - 25\% = 50\%$ of the valid votes.
3. Calculate Total Registered Voters (V)
- The margin is given as 322 votes.
- Therefore, 50% of Valid Votes = 322.
- $0.50 \times (\text{Valid Votes}) = 322$.
- Substitute Valid Votes = $0.736V$:
- $0.50 \times (0.736V) = 322$.
- $0.368V = 322$.
- $V = \frac{322}{0.368}$.
- $V = 875$.
Thus, the total number of registered voters is 875.
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