PLEASE! HELP STEP BY STEP ME WITH THIS WORD PROBLEM

Question

The students at Harrison Middle School are being split into groups for a community service project. The school faculty has decided that each grade (6th, 7th, and 8th) will be split up into their own set of groups. The faculty has also decided that it is important for each grade to be split evenly into groups, with no leftover students, so that each group in a grade has exactly the same number of boys and girls. For each of the following grades, determine the largest number of groups that can be made and the number of boys and girls that will be in each group.

1. The 6th grade has 64 girls and 72 boys.
2. The 7th grade has 81 girls and 63 boys.
3. The 8th grade has 68 girls and 60 boys.

Answer 1

You are looking for the greatest common factor for each grade level.

First find the factors for each group of students.

6th grade has 64 girls and 72 boys

Factors for 64 girls = Factors for 72 boys =

1 X 64 1 x 72

2 X 32 2 X 36

4 X 16 3 X 24

8 X 8 4 X 18

6 X 12

8 X 9

Which is the largest factor that is in both groups....8

6th grade would have 8 groups. Each group would have 8 girls and 9 boys.

Follow the same steps for the 7th and 8th grade and you will have your answer.

Answer 2

Determine the greatest common factor of each number.

6th grade is done as an illustrative example

64 = 2⁶

72 = 3² • 2³

^{GCF is 8}

^{8 groups each with 8 boys and 9 girls}