Question

Два брата собрали некоторое количество ольховых шишек .Если старший брат отдаст младшему 6 шишек,то количество шишек у них сравняется. Если же младший отдаст старшему 6 шишек, то у старшего из станет в два раза больше, чем у младшего. Сколько шишек собрал каждый из них? (решение без уравнения)

Answer 1

Всего у два брата 12 шишек. у 1 6шишек я у 2 тоже 6

Answer 2

Problem Analysis

Two brothers have collected a certain number of alder cones. If the older brother gives 6 cones to the younger brother, the number of cones will be equal. If the younger brother gives 6 cones to the older brother, the older brother will have twice as many cones as the younger brother. We need to determine how many cones each of them collected.

Solution

Let's assume the number of cones collected by the older brother is x and the number of cones collected by the younger brother is y.

According to the problem statement, if the older brother gives 6 cones to the younger brother, the number of cones will be equal. This can be represented as:

x - 6 = y + 6 (Equation 1)

Similarly, if the younger brother gives 6 cones to the older brother, the older brother will have twice as many cones as the younger brother. This can be represented as:

x + 6 = 2(y - 6) (Equation 2)

We can solve this system of equations to find the values of x and y.

Solving the System of Equations

Let's solve the system of equations using substitution.

From Equation 1, we can express x in terms of y:

x = y + 12 (Equation 3)

Substituting Equation 3 into Equation 2:

(y + 12) + 6 = 2(y - 6)

Simplifying the equation:

y + 18 = 2y - 12

Bringing all the terms to one side:

2y - y = 18 + 12

Simplifying further:

y = 30

Substituting the value of y back into Equation 3:

x = 30 + 12 = 42

Therefore, the older brother collected 42 cones and the younger brother collected 30 cones.

Answer

The older brother collected 42 cones and the younger brother collected 30 cones.

Explanation

According to the given conditions, if the older brother gives 6 cones to the younger brother, the number of cones will be equal. Similarly, if the younger brother gives 6 cones to the older brother, the older brother will have twice as many cones as the younger brother. By solving the system of equations, we found that the older brother collected 42 cones and the younger brother collected 30 cones.