high school musical

Question

there is only one freshmen in the cast of the high school musical. There are 6 sophomores and 11 juniors. One third of the cast are seniors. How many seniors are in the musical.

Answer 1

1 freshman+6 sophomores+11 juniors accounts for 2/3 of the cast because 1/3 are seniors

1+6+11=18

18 is 2/3 of what number ?

let x=# of cast members

(2/3)x=18

(3/2)(2/3)x=(3/2)(18)

x=27 cast members in all

1/3 are seniors, (1/3)*27=9 seniors, or, 27-18=9 seniors again

Answer 2

Let x = the number of seniors in the play. Since the seniors comprise 1/3 of the cast, the total cast = 3x:

 

(1 freshman) + (6 sophomores) + (11 juniors) + (x seniors) = 3x castmembers

 

18 + x = 3x

 

Solve for x.