An arts academy requires there to be 3 teachers for every 57 students and 4 for every 44 students. How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 121 students?

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Complete Question

An arts academy requires there to be 3 teachers for every 57 students and 4 tutors for every 44 students. How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 121 students?

a)19 students per teacher

b)11 students per tutor

c)11 tutors if they have 121 students

Step-by-step explanation:

An arts academy requires there to be 3 teachers for every 57 students and 4 tutors for every 44 students.

a) How many students does the academy have per teacher?

3 teachers for every 57 students

3 teachers = 57 students

1 teacher = x

Cross Multiply

3x = 1 × 57 students

x = 57 students/3

x = 19 students

Hence, we have 19 students per teacher

b) How many students Per tutor?

4 tutors for every 44 students.

4 tutors = 44 students

1 tutor = x students

Cross Multiply

4x = 44 × 1

x = 44/4

x = 11 students.

This means that we have 11 students per tutor

c) How many tutors does the academy need if it has 121 students?

4 tutors for every 44 students.

44 students = 4 tutors

121 students = x

Cross Multiply

x = 121 × 4/44

x = 11 tutors

Hence, the school would need 11 tutors if they have 121 students

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,

exactly you go it

step-by-step explanation: