Question

During first semester, the ratio of the number of students in our class to the number of students in gym class was 2 to 7. However, the art classes were really small, and the gym classes with large, so the principal change the students classes for second semester. In second semester, the ratio of the number of students in our class to the number of students in gym class was 5 to 4. If 75 students were in our class second semester, how many were in our class in gym class first semester.

Answer 1

5/4 = 75/x....5 in art to 7 in gym = 75 in art to x in gym
cross multiply
5x = 300
x = 300/5
x = 60..... according to 2nd semester, there are 75 in art and 60 in gym....total of (75 + 60) = 135 total students in the two classes.

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