The ratio of boarders to day students at a school was originally 5 to 12. However, after a number of new boarders join the initial 150 boarders, the ratio changed to 1 to 2. If no boarders became day students and vice versa, and no students left the school, how many new boarders joined the school?  Select the correct option.
A) 30
B) 50
C) 70
D) 80
E) 90

Rationale: "let x be the number of new boarders . the ratio changed from 5 : 12 up to 1 : 2 = 6 : 12 . 150 / ( 150 + x ) = 5 / 6 x = 30 the answer is a ."
Answer: A