Question 1156292: 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.
The 6th grade has 64 girls and 72 boys.
The 7th grade has 81 girls and 63 boys.
The 8th grade has 68 girls and 60 boys.
Please show me step by how to solve this problem, so I will be able to solve the other problems like this.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
The 6th grade has 64 girls and 72 boys.
The 7th grade has 81 girls and 63 boys.
The 8th grade has 68 girls and 60 boys.
Please show me step by step how to solve this problem, so I will be able to solve the other problems like this.
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6th grade problem::
Find the greatest common devisor of 64 and 72
64 = 2^6;;;; 72 = 2^3*3
^2
The GCD is 2^3 or 8
Ans:: 8 groups each with 8 girls and 9 boys
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7th grade problem:
81 = 3^4:::: 63 = 3^2*7
The GCD is 3^2 = 9
Ans: 9 groups each with 9 girls and 7 boys
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8th grade::
68 = 2^2*17;;;;; 60 = 2^2*3*5
The GCD is 2^2 = 4
Ans:: 4 groups each with 17 girls and 15 boys
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Cheers,
Stan H.
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