Question

Брат и сестра собирали марки. У них вместе на 20 марок больше, чем у брата, и на 12 марок больше, чем у сестры. Сколько марок у каждого и сколько марок у них вместе?

Answer 1

Problem Analysis

We are given that a brother and sister collect stamps. Together, they have 20 more stamps than the brother alone, and 12 more stamps than the sister alone. We need to determine how many stamps each of them has and the total number of stamps they have together.

Solution

Let's assume the number of stamps the brother has is B and the number of stamps the sister has is S.

According to the given information, we have two equations: 1. The total number of stamps they have together is 20 more than the number of stamps the brother has: B + S = B + 20. 2. The total number of stamps they have together is 12 more than the number of stamps the sister has: B + S = S + 12.

We can solve these equations simultaneously to find the values of B and S.

Solving the Equations

Let's solve the equations using the substitution method.

From equation 1, we have B + S = B + 20. Rearranging the equation, we get S = 20.

Substituting the value of S in equation 2, we have B + 20 = S + 12. Substituting the value of S from equation 1, we get B + 20 = 20 + 12. Simplifying the equation, we have B + 20 = 32. Subtracting 20 from both sides, we get B = 12.

Therefore, the brother has 12 stamps (B = 12) and the sister has 20 stamps (S = 20).

Total Number of Stamps

To find the total number of stamps they have together, we can add the number of stamps the brother and sister have: B + S = 12 + 20. Simplifying the equation, we have B + S = 32.

Therefore, the brother and sister together have 32 stamps.

Answer

The brother has 12 stamps, the sister has 20 stamps, and they have 32 stamps together.

Answer 2

Пусть x обозначает количество марок у брата, а y - количество марок у сестры.

Из условия задачи известно, что у них вместе на 20 марок больше, чем у брата, и на 12 марок больше, чем у сестры. Мы можем записать это в виде уравнений:

x + y + 20 = x + (y + 12)

Раскроем скобки и упростим уравнение:

x + y + 20 = x + y + 12

Удалим одинаковые слагаемые с обеих сторон уравнения:

20 = 12

Это уравнение не имеет решений. Возможно, в условии задачи допущена ошибка или пропущена информация. Пожалуйста, проверьте условие задачи и предоставьте дополнительные данные, если они доступны.