At a talent show, 3/5 of the acts were singing. One-third of the remaining acts were instrumental. See description!

Question

At a talent show, 3/5 of the acts were singing. One-third of the remaining acts were instrumental. If 12 acts were instrumental, how many acts were in the talent show?

Answer 1

3/5 were singing. That leaves 2/5 of the acts remaining

 

1/3 of 2/5 = (1/3)(2/5) = 2/15

 

2/15 of the acts were instrumental

 

(2/15)x=12     (x = total acts)

 

multiply both sides by 15/2 (the reciprocal of 2/15)

 

x = 12(15/2) = 90

 

There was a total of 90 acts