Question

Дети,построенные парами,вышли из парка,Где собирали листья для гербария .В каждой паре идут мальчик и девочка,при этом у мальчика либо ровно в два раза больше листьев,Чем у девочек,либо впятерт меньше.Может ли оказаться так что ,в сумме у всех детей ровно 2015 листьев?

Answer 1

Нет, не может.
В каждой паре количество листьев КРАТНО либо (1+2=) 3, либо (1+5= ) 6.
Значит, ОБЩЕЕ количество листьев у ВСЕХ пар ДОЛЖНО ДЕЛИТЬСЯ на 3.

Но число 2015 НЕ ДЕЛИТСЯ на 3...

Answer 2

Problem Analysis

We are given that pairs of children, consisting of a boy and a girl, leave a park where they collected leaves for a herbarium. The number of leaves the boys have is either exactly twice as many as the girls, or one-fifth of the number of leaves the girls have. We need to determine if it is possible for the total number of leaves collected by all the children to be exactly 2015.

Solution

Let's assume that there are 'x' pairs of children. We can represent the number of leaves the girls have as 'g' and the number of leaves the boys have as 'b'. According to the given conditions, we have two equations:

1. b = 2g (The number of leaves the boys have is exactly twice as many as the girls) 2. b = (1/5)g (The number of leaves the boys have is one-fifth of the number of leaves the girls have)

To find a solution, we need to find values of 'g' and 'b' that satisfy both equations and also make the total number of leaves equal to 2015.

Let's solve the equations to find the possible values of 'g' and 'b':

From equation 1, we have b = 2g.

From equation 2, we have b = (1/5)g.

Setting the two equations equal to each other, we get:

2g = (1/5)g

Simplifying, we find:

10g = g

This implies that 'g' must be equal to zero. However, since we are dealing with a real-world scenario, it is not possible for the girls to have zero leaves.

Therefore, it is not possible for the total number of leaves collected by all the children to be exactly 2015.

Conclusion

Based on the given conditions, it is not possible for the total number of leaves collected by all the children to be exactly 2015.