#### Answer

Candidate A is selected as the winner using the plurality-with-elimination method.

#### Work Step by Step

With the plurality-with-elimination method, the candidate with the fewest number of first-place votes is eliminated after each round. After that candidate is eliminated, the other candidates ranked below that candidate on each ballot move up one spot. The rounds continue in this way until only one candidate remains, and this candidate is declared the winner.
In round 1, we can count the number of first-place votes for each candidate.
Candidate A: 180
Candidate B: 100
Candidate C: 30
Candidate D: 40
In round 1, Candidate C has the fewest number of first-place votes, so Candidate C is eliminated. After Candidate C is eliminated, the other candidates ranked below Candidate C on each ballot move up one spot.
In round 2, we can count the number of first-place votes for each candidate.
Candidate A: 180
Candidate B: 100 + 30 = 130
Candidate D: 40
In round 2, Candidate D has the fewest number of first-place votes, so Candidate D is eliminated. After Candidate D is eliminated, the other candidates ranked below Candidate D on each ballot move up one spot.
In round 3, we can count the number of first-place votes for each candidate.
Candidate A: 180
Candidate B: 100 + 40 + 30 = 170
In round 3, Candidate B has the fewest number of first-place votes, so Candidate B is eliminated. After Candidate B is eliminated, Candidate A is the only candidate remaining, so Candidate A is declared the winner.
Candidate A is selected as the winner using the plurality-with-elimination method.