Election Voter Calculation: Finding Registered Voters

This problem involves calculating the total number of registered voters based on turnout percentages and vote distribution among candidates.

Step-by-Step Vote Calculation

• Let $V$ represent the total number of registered voters.
• The number of voters who actually voted (cast votes) is 60% of $V$. $ \text{Cast Votes} (C) = 0.60 \times V $
• Candidate X received 40% of the cast votes ($C$). $ \text{Votes for X} = 0.40 \times C $
• The remaining cast votes were split equally among the other three candidates. $ \text{Remaining Votes Percentage} = 100\% - 40\% = 60\% $
• Each of the other three candidates received $60\% / 3 = 20\%$ of the cast votes ($C$). $ \text{Votes for Each Other Candidate} = 0.20 \times C $
• Candidate X received 480 more votes than each of the other candidates. The difference in the percentage of cast votes is $40\% - 20\% = 20\%$. $ \text{Difference in Votes} = (\text{Votes for X}) - (\text{Votes for Each Other Candidate}) = 480 $ $ (0.40 \times C) - (0.20 \times C) = 480 $ $ 0.20 \times C = 480 $
• Solve for the number of cast votes ($C$): $ C = \frac{480}{0.20} $ $ C = 2400 $
• Now, use the cast votes ($C$) to find the total number of registered voters ($V$). We know $C = 0.60 \times V$. $ 2400 = 0.60 \times V $
• Solve for $V$: $ V = \frac{2400}{0.60} $ $ V = 4000 $

Therefore, there were 4000 registered voters.