Question

Решите пожалуйста задачу способом подстановки. Площадь, занятая плодовыми деревьями, на 6 га больше, чем площадь, занятая овощами. После того как площадь, занятую плодовыми деревьями, увеличали на 25%, а площадь, занятую овощами на 20%, сумма этих площадей стала равной 32 га. Найдите персональную площадь, занятую плодовыми деревьями, и первоначальную площадь, занятую овощами.

Answer 1

!х га - первонач. площадь под овощамих+6 га - первонач. площадь занимали деревьях+6+0,25(х+6)+х+0,2х=322,45х=24,5х=10(га) -первоначальная площадь под овощами10+6=16(га) - первонач. площадь занимали деревья

Answer 2

Problem Analysis

We are given that the area occupied by fruit trees is 6 hectares (ha) more than the area occupied by vegetables. After increasing the area occupied by fruit trees by 25% and the area occupied by vegetables by 20%, the sum of these areas becomes 32 ha. We need to find the area occupied by fruit trees before the increase and the initial area occupied by vegetables.

Solution

Let's assume the initial area occupied by vegetables is x ha. According to the problem, the area occupied by fruit trees is 6 ha more than the area occupied by vegetables, so the area occupied by fruit trees is x + 6 ha.

After increasing the area occupied by fruit trees by 25%, the new area occupied by fruit trees becomes 1.25 * (x + 6) ha. Similarly, after increasing the area occupied by vegetables by 20%, the new area occupied by vegetables becomes 1.2 * x ha.

According to the problem, the sum of the new areas occupied by fruit trees and vegetables is 32 ha. Therefore, we can write the equation:

1.25 * (x + 6) + 1.2 * x = 32

Now, let's solve this equation to find the values of x and x + 6.

Solution Steps

1. Write the equation based on the problem statement: 1.25 * (x + 6) + 1.2 * x = 32 2. Simplify the equation: 1.25x + 7.5 + 1.2x = 32 3. Combine like terms: 2.45x + 7.5 = 32 4. Subtract 7.5 from both sides: 2.45x = 24.5 5. Divide both sides by 2.45: x = 10 6. Calculate the area occupied by fruit trees: x + 6 = 10 + 6 = 16

Answer

The area occupied by fruit trees before the increase is 16 hectares (ha), and the initial area occupied by vegetables is 10 hectares (ha).