Question

During first semester, the ratio of the number of students 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 principal 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? *

Answer 1

arts : gym = 2:7 = 2x : 7x

second semester:
arts : gym = 5y : 4y
5y = 75
y = 15
so in 2nd semester: 75 arts and 60 gym

assuming that there 135 students in both semesters, and students were
simply shuffled around, we have to split those 135 into a ratio of 2:7

2x + 7x = 135
9x = 135
x = 15

so in the first semester
2x = 30
7x = 105

Horrible decision by principal, as if there is no difference between
studying art and taking gym!

Answer 2

and what about shop classes?