Question

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

Answer 1

The music director could make 15 groups of performers with 6 6th grade students and 5 7th grade students in each group.

Explanation:

Since in the question it is mentioned that

There is 90 6th grade students and 75 7th grade students

Now factor could be done in the following ways

90 = 2 × 45 = 2 × 3 × 15 = 2 × 3 × 3 × 5

75 = 3 × 25 = 3 × 5 × 5

Now the GCF of 90 and 75 is

= 3 × 5

= 15

So,

90 = 15 × 6

75 = 15 × 5

Hence, The music director could make 15 groups of performers with 6 6th grade students and 5 7th grade students in each group.