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 first semester

Answer 1

5/4 = 75/g....cross multiply because this is a proportion
5g = 300
g = 300/5
g = 60
so in 2nd semester, there were 75 students in art class and 60 students in gym class....for a total of 135 students.

1st semester....ratio was 2:7...added = 9
art : 2/9(135) = 270/9 = 30 <=== art class had 30
gym: 7/9(135) = 945/9 = 105 <=== gym class had 105