There are 30 violin students, 1/3 as many viola students as violin students, and 1/5 as many cello students as violin students. How many students are in all?

Question

I said 30 violin students, 40 for viola, and 36 for cello.
1/3 of 30= 10 (10+30)
1/5 of 30= 6. (6 +30)
It should be 30+ 40+ 36= 106 students
The teacher said its 46. Help.

Answer 1

You do not add another 30 to each of the fractions.

30 + 30/3 + 30/5 = 30 + 10 + 6 = 46