Question

A physical education teacher plans to divide the seventh graders at Wilson Middle School into teams of equal size of year-ending mock Olympic event. He wants each team to have between 5 and 9 students, and has a strong preference to have the same number of students on each team. The seventh grade at Wilson consists of three classes, one with 24 stu- dents, one with 26, and one with 21. How many students should be on each team?

Answer 1

Explanation:

Consider the provided information.

The total number of students are: 24+26+21=71

He wants each team will have the same number of students between 5 and 9.

The number between 5 to 9 are 6, 7 and 8.

The number 71 is a prime number so we need to divide the 71 students in group so that minimum students left without team.

Dividing 6 students in each group.

Number of teams:
`(71)/(6)` = 11 teams and 5 students.

Dividing 7 students in each group.

Number of teams:
`(71)/(7)` = 10 teams and 1 students.

Dividing 8 students in each group.

Number of teams:
`(71)/(8)` = 8 teams and 7 students.

Thus, we can not divide 71 students into equal teams, but 70 divided by 7 gives the least students left out i.e 10 teams each with 7 students and only 1 student will remain at last.