Question

Решите задачу арифметическим м алгебраическим способами. Решение арифметическим способом дополните пояснением, какие действия над величинами были выполнены. " В одной бочке на 5 л бензина больше, чем в другой. Когда в первую долили 10 л, а во вторую 35 л, во второй стало в 2 раза больше бензина, чем в первой. Сколько бензина было в каждой бочке первоначально?"

Answer 1

Пусть в первой бочке х литров, тогда во второй х+5
2(х+10)=(х+5)+35
2х+20=х+40
2х-х=40-20
х=10- в первой

10+5=15- во второй

Answer 2

Problem Analysis

We are given two barrels, one containing 5 liters more gasoline than the other. After pouring 10 liters into the first barrel and 35 liters into the second barrel, the second barrel contains twice as much gasoline as the first barrel. We need to determine the initial amount of gasoline in each barrel.

Solution

Let's assume that the initial amount of gasoline in the first barrel is x liters. Since the second barrel contains 5 liters more than the first barrel, the initial amount of gasoline in the second barrel is x + 5 liters.

After pouring 10 liters into the first barrel, it will contain x + 10 liters of gasoline. Similarly, after pouring 35 liters into the second barrel, it will contain x + 5 + 35 liters of gasoline.

According to the problem, the second barrel contains twice as much gasoline as the first barrel after pouring. Therefore, we can set up the following equation:

(x + 5 + 35) = 2(x + 10)

Now, let's solve this equation to find the value of x.

Expanding the equation:

x + 40 = 2x + 20

Simplifying the equation:

40 - 20 = 2x - x

20 = x

So, the initial amount of gasoline in the first barrel is 20 liters.

Since the second barrel contains 5 liters more than the first barrel, the initial amount of gasoline in the second barrel is 20 + 5 = 25 liters.

Therefore, initially, there were 20 liters of gasoline in the first barrel and 25 liters of gasoline in the second barrel.

Explanation of Arithmetic Method

In the arithmetic method, we used algebraic equations to represent the given information and solve for the unknowns. We made the assumption that the initial amount of gasoline in the first barrel is x liters. Based on this assumption, we expressed the initial amount of gasoline in the second barrel as x + 5 liters.

We then used the information about the amount of gasoline poured into each barrel to set up an equation. By equating the amount of gasoline in the second barrel after pouring to twice the amount in the first barrel after pouring, we obtained an equation that we could solve for x.

Solving the equation, we found that x = 20, which represents the initial amount of gasoline in the first barrel. We then calculated the initial amount of gasoline in the second barrel by adding 5 liters to x, resulting in 25 liters.

Therefore, the arithmetic method involved setting up and solving equations to find the unknowns and determine the initial amounts of gasoline in each barrel.