Question

A physical education teacher plans to divide the seventh graders at Wilson Middle School into teams of equal size for a year-ending mock Olympic event. He wants each team to have between 4 and 8 students, and all teams need to have the same number of students. The seventh grade at Wilson consists of three classes; one with 33 students, one with 34, and one with 22. How many students should be on each team?

a) 6 students should be on each team
b) 7 students should be on each team
c) It is not possible to divide the seventh graders into teams of equal size
d) 8 students should be on each team

Answer 1

After reviewing the possible team sizes from 4 to 8, the only number that allows the 89 seventh graders to be divided into teams of equal size without any remainder is 6. Therefore, the teams should each have 6 students (option a).

Step-by-step explanation:

To determine how many students should be on each team at the Wilson Middle School mock Olympic event, we need to find a number between 4 and 8 that evenly divides the total number of seventh graders from all classes. The three classes have 33, 34, and 22 students, respectively, which totals to 89 students when combined. We will now check if there is a number between 4 and 8 that 89 is divisible by to create teams that all have the same number of students.

• If we divide 89 by 4, we get a quotient of 22 with a remainder of 1.
• If we divide 89 by 5, we get a quotient of 17 with a remainder of 4.
• If we divide 89 by 6, we get a quotient of 14 with a remainder of 5. Since 89 is divisible by 6 with a remainder, this is a potential option for team size.
• If we divide 89 by 7, we get a quotient of 12 with a remainder of 5. The total number of students is not divisible by 7.
• If we divide 89 by 8, we get a quotient of 11 with a remainder of 1.

Only one of these numbers, 6, allows us to evenly divide the 89 students into teams with no remainder. Therefore, the correct answer is 6 students should be on each team.