Question

Составьте систему уравнений и решите её способом сложения. В двух бидонах 28 л жидкости. Если из первого бидона перелить 2 л жидкости во второй, то объём жидкости в обоих бидонах будет одинаковым. Сколько литров жидкости было в каждом бидоне первоначально?

Answer 1

Х л в 1 бидоне, у л - во 2 бидоне. Т.к. в двух бидонах 28 л , то х+у=28. из 1 бидона перелили во 2й 2л, объем жидкости в бидонах стал одинаковым, т.е. х-2=у+2. составляем систему
х+у=28
х-2=у+2

х+у=28
х-у=4

2х=32
х=15

х=16
16-у=4

х=16
у=12
16 л было в 1 бидоне первоначально, 12 л - во 2

Answer 2

Problem Analysis

We are given two containers with a total volume of 28 liters of liquid. If we transfer 2 liters of liquid from the first container to the second container, the volume of liquid in both containers will be the same. We need to determine the initial volume of liquid in each container.

Mathematical Representation

Let's represent the initial volume of liquid in the first container as x liters and the initial volume of liquid in the second container as y liters.

According to the given condition, if we transfer 2 liters of liquid from the first container to the second container, the volume of liquid in both containers will be the same. This can be represented as:

x - 2 = y + 2

We also know that the total volume of liquid in both containers is 28 liters. This can be represented as:

x + y = 28

We can solve these two equations simultaneously to find the values of x and y.

Solving the Equations

To solve the system of equations, we can use the method of addition. We'll add the two equations together to eliminate the variable y.

Adding the equations: (x - 2) + (x + y) = (y + 2) + (x + y)

Simplifying: 2x - 2 = 2y + 4

Rearranging the equation: 2x - 2y = 6

Now, we have a new equation that relates x and y. We can use this equation along with the second equation to solve for x and y.

Substituting the value of x + y from the second equation into the new equation: 2x - 2(28 - x) = 6

Simplifying: 2x - 56 + 2x = 6

Combining like terms: 4x - 56 = 6

Adding 56 to both sides: 4x = 62

Dividing both sides by 4: x = 15.5

Substituting the value of x back into the second equation to find y: 15.5 + y = 28

Subtracting 15.5 from both sides: y = 12.5

Solution

The initial volume of liquid in the first container was 15.5 liters, and the initial volume of liquid in the second container was 12.5 liters.

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