Question

Для продажи весь картофель расфасовали в 10 пакетов, по 2 кг и по 3 кг. Масса всех пакетов по 2 кг оказалась равной массе всех пакетов по 3 кг. Сколько было пакетов каждого вида?

Answer 1

Ответ: можно методом подбора 6 мешков по 2 килограмма и 4 мешка по 3 килограмма по весу получаются 12 кг каждый

Answer 2

Problem Analysis

We are given that all the potatoes were divided into 10 bags, with some bags containing 2 kg of potatoes and others containing 3 kg of potatoes. The total weight of the bags with 2 kg potatoes is equal to the total weight of the bags with 3 kg potatoes. We need to determine the number of bags of each type.

Solution

Let's assume the number of bags with 2 kg of potatoes is x and the number of bags with 3 kg of potatoes is y.

From the given information, we can set up the following equations:

1. The total number of bags is 10: x + y = 10. 2. The total weight of the bags with 2 kg potatoes is equal to the total weight of the bags with 3 kg potatoes: 2x = 3y.

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

Solving the Equations

To solve the system of equations, we can use the substitution method.

From equation 1, we can express x in terms of y: x = 10 - y.

Substituting this value of x into equation 2, we get: 2(10 - y) = 3y.

Simplifying the equation: 20 - 2y = 3y.

Bringing all the y terms to one side: 20 = 5y.

Dividing both sides by 5: y = 4.

Substituting this value of y back into equation 1, we get: x + 4 = 10.

Simplifying the equation: x = 6.

Therefore, there were 6 bags with 2 kg of potatoes and 4 bags with 3 kg of potatoes.

Answer

There were 6 bags with 2 kg of potatoes and 4 bags with 3 kg of potatoes.