There Are 280 Voting Members in Your School's Faculty Union

Short Answer

There are 280 voting members in your school's faculty union. Resort Alpha (A), Resort Beta (B), Resort Gamma (G) and Resort Delta (D) are the four possible resorts at which the union could hold its annual meeting. Each faculty member ranks the four resorts, and the Method of Plurality is being used to determine which resort will be chosen. Suppose that 30 % of all members vote for Resort Alpha (A) as their 1^st choice. Assuming that all 280 members vote, then what is the smallest number of the remaining 1^st choice votes needed in order to guarantee that Resort Beta (B) is the winner?