Question

A school chorus has 90 sixth-graders and 75 seventh-graders. The music director wants to make groups with the same combination of sixth- and seventh-grade students in each group. What is the largest number of groups that could be formed? If that many groups are formed, how many students of each grade level would be in each group?

Answer 1

The largest number of groups that could be formed is 15, with 6 sixth-graders and 5 seventh-graders in each group.

Step-by-step explanation:

To find the largest number of groups that can be formed with the same combination of sixth- and seventh-grade students, we need to find the greatest common divisor (GCD) of the number of sixth-graders and seventh-graders. The GCD of 90 and 75 is 15. Therefore, the largest number of groups that could be formed is 15.

Each group will have an equal number of sixth- and seventh-graders. To find the number of students of each grade level in each group, we divide the total number of each grade by the number of groups. The number of sixth-graders in each group is 90 divided by 15, which is 6. The number of seventh-graders in each group is 75 divided by 15, which is 5.