Students were surveyed about their favorite colors 1\4 of the student preferred red, 1/8 student of the students preferred blue and 3/5 of the remaining students preferred green. if 15 students preferred green how many students were surveyed?

All we have to find the fraction of students who preferred green and go from there.
Subtracting blue and red out of the all students,
1- (1/8+1/4)
1- 3/8
5/8 is the remaining students, in order to find 3/5 of the remaining students, we multiply by 3/5

5/8(2/5) = 3/8
3/8 preferred green, which was 15 students. In order to get 100% of the whole  population (1), we multiply by 8/3:

15(8/3) = 40

40 students were surveyed in total.