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. If the largest group was formed, how many students of each grade level would be in each group?

Answer 1

The music director can form a total of 15 groups

6 Sixth grade students per group

5 Seventh grade students per group

Explanation:

Sixth grade students = 90

Seventh grade students = 75

Find the highest common factor of 75 and 90

90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.

75 = 1, 3, 5, 15, 25, 75

The highest common factor of 75 and 90 is 15

Therefore, the music director can form a total of 15 groups

Sixth grade students per group = 90 / 15

= 6 Sixth grade students per group

Seventh grade students per group = 75 / 15

= 5 Seventh grade students per group