Question

An arts academy requires there to be 3 teachers for every 45 students and 4 tutors for every 36 students. How many students does the academy have per​ teacher? Per​ tutor? How many tutors does the academy need if it has 54 students

Answer 1

The arts academy has 15 students per teacher and 9 students per tutor. To accommodate 54 students, the academy would need 6 tutors based on the given ratios.

Let's calculate the students per teacher and students per tutor for the arts academy based on the given information.

For teachers:

The ratio is 3 teachers for every 45 students. Therefore, the number of students per teacher is
`\( (45)/(3) = 15 \)` students per teacher.

For tutors:

The ratio is 4 tutors for every 36 students. Therefore, the number of students per tutor is
`\( (36)/(4) = 9 \)` students per tutor.

Now, if the academy has 54 students, we can calculate the number of tutors needed:

`\( \text{Number of tutors needed} = \frac{\text{Total students}}{\text{Students per tutor}} = (54)/(9) = 6 \) tutors needed.`

In summary, the arts academy has 15 students per teacher, 9 students per tutor, and it would need 6 tutors for a total of 54 students.