Question

для обработки поля площадью 600 га его разделили между тремя бригадами так,что вторая бригада получила участок в 3 раза,а третья в 2 раза больше первой. Сколько гектаров должна обработать каждая бригада. решить задачу алгебраическим способом

Answer 1

Problem Analysis

We are given a field with an area of 600 hectares that needs to be divided among three brigades. The second brigade receives a plot that is three times larger than the first brigade, and the third brigade receives a plot that is two times larger than the first brigade. We need to determine the area that each brigade should cultivate.

Solution

Let's assume that the area cultivated by the first brigade is x hectares.

According to the problem, the second brigade receives a plot that is three times larger than the first brigade. Therefore, the area cultivated by the second brigade is 3x hectares.

Similarly, the third brigade receives a plot that is two times larger than the first brigade. Therefore, the area cultivated by the third brigade is 2x hectares.

The sum of the areas cultivated by all three brigades should equal the total area of the field, which is 600 hectares. We can write this as an equation:

x + 3x + 2x = 600

Simplifying the equation:

6x = 600

Dividing both sides of the equation by 6:

x = 100

Therefore, the first brigade should cultivate 100 hectares, the second brigade should cultivate 300 hectares, and the third brigade should cultivate 200 hectares.

Answer

Each brigade should cultivate the following areas: - First brigade: 100 hectares - Second brigade: 300 hectares - Third brigade: 200 hectares