A Board of Adjustment is hereby established which shall consist of seven members. The term of office of the members of the Board and the manner of their appointment shall be as provided by statute. Vacancies shall be filled for the unexpired term of any member whose term becomes vacant. Two members shall be residents of the area outside the City limits which is subject to this chapter. Said members shall be appointed by the County Board of Supervisors. A majority of the members of the Board of Adjustment shall be persons representing the public at large and shall not be involved in the business of purchasing or selling of real estate.