There are 60 grade 8 students and 40 grade 7 students.

Question

There are 60 grade 8 students and 40 grade 7 students. These students need to be divided into groups with the same number of grade 8 and 40 grade 7 students in each group. How many different ways can this be achieved? Describe these groups if possible.

Answer 1

Hi Zina,

 

The question is asking if the students can be divided into 2 groups and/or 4 groups and or 6 groups . . .

 

The number of groups should be an even number and a  common factor for 60 and 40.  So you can't have 40 people in one group because 40 doesn't go into 60.

 

So what even numbers do go into 40 & 60?

 

2, 4, 10 and 20

 

So you can 2 groups where each group as 30 grade 8 students and 20 grade 7 students

 

4 groups where each group as 15 grade 8 students and 10 grade 7 students.

 

How many grade 8 and grade 7 students are there in each of the 10 groups and each of the 20 groups?

 

Dan

 

After thinking a little more about this question, you can also use the odd number of groups that factor into 60 and 40.

 

Can you think of any?