Percentages

Step 1: Determine the vote share for each candidate. Assuming all votes went to one of the two candidates: Losing candidate's share = 30% of total votes. Winning candidate's share = 100% - 30% = 70% of total votes.

Step 2: Calculate the difference in vote share (the margin of victory). Margin = Winning % - Losing % = 70% - 30% = 40%.

Step 3: Equate the margin percentage to the actual vote difference. We are given that the margin of victory is 15,000 votes. Therefore, 40% of the total votes corresponds to 15,000.

Step 4: Calculate the number of votes for the winning candidate. We need to find the value of 70% of the total votes. We can set up a proportion: If 40% = 15,000 votes, Then 1% = votes. So, 70% = votes. The winning candidate received 26,250 votes.