in rsm camp, there are four counselors for every fifty seven students and three teachers for every five counselors.

write the ratio of students to counselors to teachers, respectively.

Students : Counselors : Teachers = 285: 20 : 12

Step-by-step explanation:

In the camp, the ratio of:

( C: S )  Counselors : Students   is  4   :  57

( T: C )  Teachers :   Counselors  is  3   :  5

To determine the ratio of   -  Students : Counselors : Teachers

Here given      -  C : S  = 4 : 57

Multiplying both sides by 5, we get

C: S  = 4 x 5  : 57 x 5  = 20 : 285

So, for every 20 counselors, there are 285 students       (1)

Similarly, given   Teachers :   Counselors  is  3   :  5

Multiplying both sides by 4, we get

T  : C  = 3 x 4  : 5 x 4  = 12  : 20

So, for every 12  teachers, there are 20 Counselors       (2)

Hence, in both equation 1 and 2 the number of counselors is same = 20 .

Hence, both the ratios acne be combined.

So we get C : S  = 20 : 285      and T : C  = 12: 20

Inverting the values

⇒  S : C  = 285 : 20         and C : T  = 20 : 12

or, S : C : T  = 285: 20 : 12

or, Students : Counselors : Teachers = 285: 20 : 12

Hence, for every 285 students there are 20 counselors and 12 teachers.

(a) the volume of the cone is 20/3 in3

hence, option a is correct.