Question

В трех канистрах было 70 л бензина. В первой канистре на 10 л больше, чем во второй Когда из первой канистры 26 л перелили в третью, во второй и третьей канистрах бензину стало поровну. ВОПРОС: сколько бензина было в 1 канистре?

Answer 1

Пусть в 1 канистре было х л, во 2 канистре х-10 л, а в 3 канистре у л.
В трех канистрах было 70 л
x + x - 10 + y = 70
2x + y = 80
Когда перелили 26 л из 1 канистры в 3, во 2 и 3 бензина стало поровну.
x - 10 = y + 26
y = x - 36
Подставляем в 1 уравнение
2x + x - 36 = 80
3x = 116
x = 116/3 = 38 2/3 л - было в 1 канистре
x - 10 = 28 2/3 л - было во 2 канистре
y = x - 36 = 2 2/3 л - было в 3 канистре.

Answer 2

Пусть x - количество бензина во второй канистре. Тогда в первой канистре было x + 10 литров бензина, а в третьей канистре было 70 - (x + x + 10) = 70 - 2x - 10 = 60 - 2x литров бензина.

Когда из первой канистры перелили 26 литров бензина в третью, в первой осталось (x + 10) - 26 = x - 16 литров бензина.

Таким образом, у нас есть два уравнения: x - 16 = 60 - 2x (из первой канистры перелили 26 литров бензина в третью) x = 22 (из второй канистры перелили 26 литров бензина в третью)

Таким образом, во второй канистре было 22 литра бензина, а в первой канистре было 22 + 10 = 32 литра бензина.

Answer 3

Problem Analysis

We are given three containers of gasoline, and the total amount of gasoline in the three containers is 70 liters. The first container has 10 liters more than the second container. When 26 liters of gasoline are poured from the first container into the third container, the second and third containers have an equal amount of gasoline. We need to find out how much gasoline was in the first container.

Solution

Let's assume the amount of gasoline in the second container is x liters. Since the first container has 10 liters more than the second container, the amount of gasoline in the first container is x + 10 liters.

After pouring 26 liters of gasoline from the first container into the third container, the second and third containers have an equal amount of gasoline. Let's denote this amount as y liters.

Now, we can set up the following equation to solve for x:

x + (x + 10) - 26 = y

Simplifying the equation, we get:

2x - 16 = y

Since the total amount of gasoline in the three containers is 70 liters, we can write another equation:

x + (x + 10) + y = 70

Simplifying the equation, we get:

2x + y + 10 = 70

Now, we have a system of two equations with two variables. We can solve this system to find the values of x and y.

Solution Steps

1. Substitute the value of y from the first equation into the second equation: 2x + (2x - 16) + 10 = 70 Simplify the equation: 4x - 6 = 70 Solve for x: 4x = 76 x = 19

2. Substitute the value of x into the first equation to find y: y = 2x - 16 y = 2(19) - 16 y = 38 - 16 y = 22

3. Now that we have the values of x and y, we can find the amount of gasoline in the first container: Amount of gasoline in the first container = x + 10 = 19 + 10 = 29 liters

Answer

The amount of gasoline in the first container is 29 liters.