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?

This question is incomplete

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

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

6(h+1)/2=a

a=area

step-by-step explanation:

its the same thing as a square or rectangle but after multiplying two sides you need to divide it by two.