(a) The city board of education shall have power to establish and maintain a system of public schools including kindergartens and playgrounds for the benefit of children who are bona fide residents of and living within the corporate limits of such city.
(b) Such children who are six years of age and less than 19 years of age on the date school opens shall be entitled to admission to the elementary, junior and senior high schools.
(c) If a kindergarten is established and maintained, children from five to eight years of age may be admitted on such terms and conditions as the city board of education may prescribe.