Question

В шестых классах 36 мальчиков и 42 девочки. Сколько существует возможностей создать группы учащихся так, чтобы во всех группах было по одинаковому числу девочек и по одинаковому числу мальчиков? Какое может быть наибольшее число таких групп?

Answer 1

1)42-36=6
больше 6 человек в группе не может быть
2)42/6=7 девочек
3)36/6=6 мальчиков

Answer 2

Calculation of the Number of Possible Groups

To determine the number of possible groups that can be created with an equal number of boys and girls in each group, we need to find the common factors of the number of boys (36) and the number of girls (42). The common factors will represent the possible group sizes.

The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, and 36. The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, and 42.

The common factors of 36 and 42 are: 1, 2, 3, 6.

Therefore, there are four possible group sizes that can be created with an equal number of boys and girls in each group: 1, 2, 3, and 6.

Maximum Number of Groups

To determine the maximum number of groups that can be created, we need to divide the total number of students by the group size.

Since we have a total of 36 boys and 42 girls, the total number of students is 36 + 42 = 78.

Let's calculate the maximum number of groups for each possible group size:

1. Group size of 1: - The maximum number of groups is equal to the total number of students, which is 78.

2. Group size of 2: - The maximum number of groups is equal to half the total number of students, rounded down to the nearest whole number. In this case, it is 78 / 2 = 39.

3. Group size of 3: - The maximum number of groups is equal to the total number of students divided by 3, rounded down to the nearest whole number. In this case, it is 78 / 3 = 26.

4. Group size of 6: - The maximum number of groups is equal to the total number of students divided by 6, rounded down to the nearest whole number. In this case, it is 78 / 6 = 13.

Therefore, the maximum number of groups that can be created with an equal number of boys and girls in each group is as follows: - For a group size of 1: 78 groups - For a group size of 2: 39 groups - For a group size of 3: 26 groups - For a group size of 6: 13 groups.

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