An arts academy requires there to be 6 teachers for every 144 students and 5 tutors for every 40 students. How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 72 students

3 teachers and 9 tutors

Step-by-step explanation:

There are 24 students per teacher and 8 students per tutor. If the academy has 72 students, then 9 tutors would be needed.

Step-by-step explanation:

We will start with the question, how many students does the academy have per teacher. To find this, we need to set up the equation. 144 will be the number of students, 6 will be the number of teachers, and x will be the number of students per teacher.

144/6=x

24=x

So, there are 24 students for every teacher.

We could also do this as a ratio. We would do the same thing. We would divide by six to get our answer.

144:6

Make the six one.

24:1

This shows that there are 24 students for every teacher.

Now to find out how many per tutor.

We will do the same thing as before, minus the ratio, though you could still use the ratio. Remember, 40 is the number of students, 5 is the number of tutors, and x is the number of students per tutor.

40\5=x

8=x

So there are 8 students per tutor.

Now we will use this knowledge to solve for how many tutors are needed if the academy has 72 students.

We will set up our equation. 72 will be the students, we will use eight since that is how many students are needed per tutor, and x will be the number of tutors needed.

72/8=x

9=x

So this means that if the academy has 72 students, then it will need 9 tutors.