Question

Аня, Таня, Ваня собирали марки. у Ани и Тани вместе 40 марок, у Тани и Вани-50, а у Вани и Ани-70. Сколько марок у Ани?

Answer 1

Аня + Таня = 40 м.

Таня + Ваня = 50 м.

Аня + Ваня = 70 м.

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I способ:

Аня + Таня = 40                          (1)

Таня + Ваня = 50                         (2)

Аня + Ваня = 70                           (3)

 

из (1) уравнения: Аня = 40 - Таня
из (2) уравнения: Ваня = 50 - Таня
подставим в (3) уравнение: 40 - Таня + (50 - Таня) = 70

 

40 - Таня + 50 - Таня = 70

90 - 2 Таня = 70

2 Таня = 90-70

2 Таня = 20

Таня = 20:2

Таня = 10 (м.) - количество марок у Тани.

Аня = 40 - Таня = 40-10=30 (м.) - количество марок у Ани.

Ваня = 50 - Таня = 50-10=40 (м.) - количество марок у Вани.

 

II способ:

1) (40+50-70):2=10 (м.) - количество марок у Тани.

2) 40-10=30 (м.) - количество марок у Ани.

3) 50-10=40 (м.) - количество марок у Вани.

Ответ: у Ани 30 марок.

Answer 2

Problem Analysis

We are given that Anya, Tanya, and Vanya collected stamps. The total number of stamps collected by Anya and Tanya together is 40, the total number of stamps collected by Tanya and Vanya together is 50, and the total number of stamps collected by Vanya and Anya together is 70. We need to find out how many stamps Anya has.

Solution

Let's assume the number of stamps Anya has is A, the number of stamps Tanya has is T, and the number of stamps Vanya has is V.

From the given information, we can write the following equations:

1. A + T = 40 (Equation 1) 2. T + V = 50 (Equation 2) 3. V + A = 70 (Equation 3)

To solve these equations, we can use a method called substitution. We can solve Equation 1 for A and substitute it into Equations 2 and 3.

From Equation 1, we have A = 40 - T.

Substituting A = 40 - T into Equation 2, we get (40 - T) + T = 50, which simplifies to 40 + T = 50. Solving for T, we find T = 10.

Substituting A = 40 - T into Equation 3, we get (40 - T) + A = 70, which simplifies to 40 - T + A = 70. Since we know T = 10, we can substitute it into the equation and solve for A:

40 - 10 + A = 70 30 + A = 70 A = 70 - 30 A = 40

Therefore, Anya has 40 stamps.

Answer

Anya has 40 stamps.