A certain high school has 500 students. Of these students, 30 are taking music, 10 are taking art, and 10 are taking both music and art. How many students are taking neither music nor art? Choose the correct choice from the following options: A) 430 B) 440 C) 450 D) 460 E) 470

Rationale: "we ' re given a series of facts to work with : 1 ) a certain high school has 500 students . 2 ) of these students : x are taking music , y are taking art , and z are taking both music and art . we ' re asked how many students are taking neither music nor art ? let ' s test x = 30 y = 10 z = 10 so , we have 30 students taking music , 10 taking art and 10 taking both music and art . 20 student taking just music 0 student taking just art 10 student taking both music and art total = 30 students we ' re asked for the total number of students who are taking neither course . that is 500 - 30 = 470 . e"
Answer: E