Question

A school chorus has 90 sixth-grade students and 75/7 grade students the music director wants to make groups of performers with the same combination of sixth and seventh grade students in each group she wants to form as many groups as possible what is the largest number of groups that could be formed explain or show your reasoning

Answer 1

The music director can make 15 groups of performers with 6 sixth grade students and 5 seventh grade students in each group.

Explanation:

A school chorus has 90 sixth-grade students and 75 seventh-grade students.

Factor these two numbers:

`90=2\cdot 45=2\cdot 3\cdot 15=2\cdot 3\cdot 3\cdot 5\\ \\75=3\cdot 25=3\cdot 5\cdot 5`

Find GCF(90,75):

`GCF(90,75)=3\cdot 5=15`

Now,

`90=15\cdot 6\\ \\75=15\cdot 5`

Therefore, the music director can make 15 groups of performers with 6 sixth grade students and 5 seventh grade students in each group.