, 2012

Candidate A received $\frac{1008}{5600}\times100\%=0.18\times100\%$ or $18\%$ of all votes. Solution 1 Since $\frac{3}{5}\times100\%=0.60\times100\%$, Candidate B received $60\%$ of all votes. Since Candidates C and D tied, they equally shared the remaining $100\%-60\%=40\%$ of the votes. Therefore, Candidate C received $\frac{1}{2}$ of $40\%$ of the votes, or $20\%$ of all votes. Solution 2 Since Candidate B received $\frac{3}{5}$ of all votes, then Candidates C and D shared the remaining $1-\frac{3}{5}=\frac{2}{5}$ of all votes. Candidates C and D tied, thus they shared equally the remaining $\frac{2}{5}$ of the votes. Therefore, Candidate C received $\frac{1}{2}$ of $\frac{2}{5}$ or $\frac{1}{2}\times\frac{2}{5}=\frac{2}{10}=\frac{1}{5}$ of the votes. Since $\frac{1}{5}\times100\%=0.20\times100\%$, Candidate C received $20\%$ of all votes. Solution 1 At 10:00 p.m., $90\%$ of 6000 votes or $\frac{90}{100}\times6000=5400$ votes had been counted. Of those 5400 votes that had been counted, Candidate E received $53\%$. Therefore at 10 p.m., $\frac{53}{100}\times5400=2862$ votes had been counted for Candidate E. Since there were only 2 candidates, the remaining $5400-2862$ or 2538 votes must have been counted for Candidate F. Thus, there were $2862-2538$ or 324 more votes counted for Candidate E than for Candidate F. Solution 2 At 10:00 p.m., $90\%$ of 6000 votes or $\frac{90}{100}\times6000=5400$ votes had been counted. Of those 5400 votes that had been counted, Candidate E received $53\%$. Since there are only 2 candidates, then Candidate F must have received the remaining $100\%-53\%$ or $47\%$. Thus, Candidate E received $53\%-47\%$ or $6\%$ more votes than Candidate F. Since there were a total of 5400 votes that had been counted at 10:00p.m., then Candidate E received $6\%$ of 5400 or 324 more votes than Candidate F. Candidate H received 40% of the votes and Candidate J received 35% of the votes. Thus, the only other candidate, G, received the remaining $100\%-40\%-35\%=25\%$ of the votes. Since Candidate G received 2000 votes representing 25% of all votes cast, then the total number of votes cast was $2000\times4=8000$ (since $25\%\times4=100\%$). Thus, Candidate H received $40\%$ of 8000 votes or $\frac{40}{100}\times8000=3200$ votes.