#### Answer

Since the plurality method leads to a tie, we need to use the Borda count method. Candidate C is declared the new mayor using the Borda count method.

#### Work Step by Step

Using the plurality method, the candidate who has the most first-place votes is declared the winner of the election. We can find the number of first-place votes for each candidate.
The number of first-place votes for Candidate A is 7500 + 4500 which is 12,000.
The number of first-place votes for Candidate B is 0.
The number of first-place votes for Candidate C is 12,000.
Candidate A and Candidate C are tied with 12,000 first-place votes. Since the plurality method leads to a tie, we need to use the Borda count method.
With the Borda count method, each candidate receives 1 point for each third-place vote, 2 points for each second-place vote, and 3 points for each first-place vote. The candidate who receives the most points is declared the winner.
We can find the total points for each candidate.
Candidate A:
3(7500 + 4500) + 2(0) + 1(12,000) = 48,000 points
Candidate B:
3(0) + 2(12,000 + 7500) + 1(4500) = 43,500 points
Candidate C:
3(12,000) + 2(4500) + 1(7500) = 52,500 points
Since Candidate C received the most points, Candidate C is declared the new mayor using the Borda count method.