A certain country is divided into 5 provinces. Each province consists entirely of Progressives and Traditionalists. If each province contains the same number of Traditionalists and the number of Traditionalists in any given province is 1/15 the total number of Progressives in the entire country, what fraction of the country is Traditionalist? Choose the correct option
A) 1 / 5
B) 1 / 3
C) 1 / 2
D) 2 / 3
E) 3 / 4

Rationale: "let p be the number of progressives in the country as a whole . in each province , the number of traditionalists is p / 15 the total number of traditionalists is 5 p / 15 = p / 3 . the total population is p + p / 3 = 4 p / 3 p / ( 4 p / 3 ) = 3 / 4 the answer is e ."
Answer: E