1600 people voted in an election and the winner got 500 votes. What percent of the total votes did the winner get? Can you guess the minimum number of candidates who stood for the election?
Given: Total votes = 1600 Winner's votes = 500
Formula: Percentage = (Winner's votes / Total votes) × 100
Substitution: Percentage = (500/1600) × 100
Calculation: = 31.25%
Answer: Winner got 31.25% of total votes.
Minimum number of candidates: Since winner got 500 votes, remaining 1100 votes must be split among other candidates such that each gets less than 500 votes. With 2 other candidates (3 total), max they can hold = 499 + 499 = 998, but 1100 > 998, so at least one would have 550 votes and win instead. With 3 other candidates (4 total), we can distribute 499 + 499 + 102 = 1100, all below 500. ∴ Minimum number of candidates = 4
Explanation
The chapter shows percentage calculation for votes. For minimum candidates, since winner got 31.25%, the remaining 68.75% must be distributed among other candidates such that no other candidate gets 31.25% or more. With 2 other candidates, the maximum they can hold is 499 + 499 = 998 votes, but 1100 > 998, so this is impossible. With 3 other candidates (4 total), we can distribute 499 + 499 + 102 = 1100, all below 500, so the winner still has the most votes.
Solution Steps
Total votes = 1600
Winner's votes = 500
Percentage = (500/1600) × 100 = 31.25%
Remaining votes percentage = 100% - 31.25% = 68.75%
Remaining votes = 1600 - 500 = 1100
For winner to win, each other candidate must have < 500 votes (at most 499)
With 2 other candidates, max votes they can hold = 499 + 499 = 998, but 1100 > 998, so 2 others are not enough
With 3 other candidates, we can distribute 499 + 499 + 102 = 1100, all below 500
Minimum number of candidates = 4