During first semester, the ratio of the number in art class to the number of students in gym class was 2: 7. however, the art classes were really small, and the gym classes were large, so the principle changed students classes for second semester. in second semester, the ratio of the number of students in art class to the number of students in gym class was 5: 4. if 75 students were in art class second semester, how many were in art class and gym class first semester?

In second semester:art class - 75 students
gym class - X students
5:4=75:X
X=75*4/5=60 - gym class
75+60=135 - all students

In first semester:art class - a students
gym class - g students2:7=a:g
7a=2g
7a-2g=0
a+g=135
9a=135
a=15
g=135-15=120

art class 15 students
gym class 120 students

Since it is stated that there are 75 students for art class in the second semester, the problem is to find the gym class which is equivalent to X.
The Ratio in Second semester is 5:4
5 = Art Class: 4 = Gym Class
5:4 = 75: x
x= (75 * 4) / 5
x= 60
Therefore the ratio of the students in art class and gym class is 5:4 or 75:60
the total number of the students are 135   In first semester the Ratio of the students of art class and gym class is 2:7
2 = art class
7 = Gym Class
Since the total Number of students are 135. We’ll look for the number of students in art class and gym class
2:7 =x:y
2+7=9
135/5 = 15
x=15
y=120
2:7 = 15:120