Question

В саду дети собирали яблоки,груши,персики и урюк.Масса всего собранного 38 кг.Масса собранных яблок и груш равна 25 кг,масса яблоков и персиков 17 кг,а масса яблок и урюка 16 кг.Сколько килограммов каждого фрукта собрали дети?

Answer 1

1)х+25-х+17-х+16-х=38

-2х+58=38

-2х=38-58

-2х=-20

х=10кг-яблок.

2)25-10=15кг-груш.

3)17-10=7кг-персиков.

4)16-10=6кг-урюка.

Answer 2

Problem Analysis

The problem states that children in a garden collected apples, pears, peaches, and uruk. The total weight of all the collected fruits is 38 kg. The weight of the collected apples and pears is 25 kg, the weight of the apples and peaches is 17 kg, and the weight of the apples and uruk is 16 kg. We need to determine the weight of each fruit collected by the children.

Solution

Let's assume the weight of apples is A kg, the weight of pears is P kg, the weight of peaches is C kg, and the weight of uruk is U kg.

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

1. A + P + C + U = 38 (equation 1) - The total weight of all the collected fruits is 38 kg. 2. A + P = 25 (equation 2) - The weight of the collected apples and pears is 25 kg. 3. A + C = 17 (equation 3) - The weight of the collected apples and peaches is 17 kg. 4. A + U = 16 (equation 4) - The weight of the collected apples and uruk is 16 kg.

To solve these equations, we can use a method called substitution. We can solve equations 2, 3, and 4 for A and substitute the values into equation 1.

From equation 2, we have A = 25 - P. Substituting this value into equation 3, we get (25 - P) + C = 17, which simplifies to C = 17 - 25 + P, or C = P - 8. Substituting the value of A from equation 2 into equation 4, we get (25 - P) + U = 16, which simplifies to U = 16 - 25 + P, or U = P - 9.

Now, we can substitute the values of A, C, and U into equation 1: (25 - P) + P - 8 + P - 9 = 38. Simplifying this equation, we get 3P - 8 - 9 + 25 = 38, which further simplifies to 3P + 8 = 38. Subtracting 8 from both sides, we have 3P = 30. Dividing both sides by 3, we get P = 10.

Now that we have the value of P, we can substitute it back into equations 2, 3, and 4 to find the values of A, C, and U.

From equation 2, we have A + 10 = 25, which gives A = 15. From equation 3, we have 15 + C = 17, which gives C = 2. From equation 4, we have 15 + U = 16, which gives U = 1.

Therefore, the children collected 15 kg of apples, 10 kg of pears, 2 kg of peaches, and 1 kg of uruk.

Answer: The children collected: - 15 kg of apples - 10 kg of pears - 2 kg of peaches - 1 kg of uruk