Question

An arts academy requires there to be 4 teachers for every 64 students and 5 tutors for every 45 students. How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 117 students?

Answer 1

16 students per teacher

13 tutors for 117 students

Step-by-step explanation

We are given that in an academy:

=> There have to be 4 teachers for every 64 students

=> There have to be 5 tutors for every 45 students

a) To find the number of students per teacher, we have to divide the total number of students by the total number of teachers.

That is:

`\begin{gathered} (64)/(4) \\ =\text{ 16 students per teacher} \end{gathered}`

b) To find the number of tutors the academy needs for 117 students, we have to first find the number of tutors per student.

That is divide the total number of tutors by the number of students:

`\begin{gathered} (5)/(45) \\ =(1)/(9)\text{ tutors per student} \end{gathered}`

Now, we multiply this by 117 students to find the number of tutors needed:

`\begin{gathered} (1)/(9)\cdot117 \\ =13\text{ tutors } \end{gathered}`

The academy needs 13 tutors for 117 students.