Ratio of the number of students in art class to the number of students in gym class was 2: 7, however art class is small, and gym class is large, students changed for the second semester. now the students in art class to the number students in gym class is 5: 4. if 75 students are in art class in second semester, how many were in art class and gym class first semester?

Semester 1:

let the number of students in the art class be 2a, and the number of the students in the gym class be 7a. (check: the ratio is 2a:7a = 2:7)

so the total number of students is 9a.

semester 2:

the 9a students are go to the art class and gym class at a a ratio of 5: 4, 

so 5a students go to the art class, and 4a students go to the gym class.

75 students are in art class in second semester means that 5a=75, 

so a=75/5=15.

In the 1st semester the number of students was: 

art class: 2a=2*15=30

gym class: 7a=7*15=105