The physical education teacher has to organize 27 grade 6 students, 36 grade 7 students, and 54 grade 8 students into groups of equal number. a) what is the greatest number of students who can be in one group? b) how many groups will there be? lesson is about greatest common factor btw: )

a 13 students

b 9 groups

Step-by-step explanation:

I will assume we want equal amounts of children from each grade

6th grade:

27 = 3*9 = 3*3*3

7th grade

36 = 4*9 = 2*2*3*3

8th grade

54 = 6*9 = 2*3*3*3

The terms that appear in each of 6th, 7th and 8th are 3*3

That is the greatest common factor

3*3 = 9

We can make 9 groups,  Factor out the 9 and what is left is the number from each grade that is in each group

6th grade:

27 = 3*9   There will be 3 6th graders in one group

7th grade

36 = 4*9   There will be 4 7th graders in one group

8th grade

54 = 6*9 = There will be 6 8th graders on one group

In one group we have 3+4+6 = 13 people

There will be 9 groups of 13 children

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)