Question

В 1 элеваторе было зерна в 3 раза больше чем в другом. Из 1 элеватора вывезли 960 тон зерна а во 2 привезли 240 тон. После чего в обоих элеваторах зерна стало поровну. Сколько зерна было в 1 и 2 элеваторе первоначально?

Answer 1

Пусть х тонн зерна было во втором элеваторе,
тогда 3х тонн зерна было в первом элеваторе.

3х - 960 = х + 240
3х - 3 = 240 + 960
2х = 1200
х = 1200 : 2
х = 600 (т) - во втором элеваторе.
600 * 3 = 1800 (т) - в первом элеваторе.
Ответ: в первом элеваторе было 1800 тонн зерна, во втором - 600 тонн зерна.

Answer 2

Problem Analysis

We are given two elevators, one with three times more grain than the other. 960 tons of grain are taken out of the first elevator, while 240 tons are brought into the second elevator. After this, the amount of grain in both elevators is equal. We need to find the initial amount of grain in each elevator.

Solution

Let's assume that the initial amount of grain in the first elevator is x tons. Since the second elevator has three times less grain, the initial amount of grain in the second elevator is x/3 tons.

After 960 tons of grain are taken out of the first elevator, the amount of grain remaining in the first elevator is x - 960 tons. Similarly, after 240 tons of grain are brought into the second elevator, the amount of grain in the second elevator is (x/3) + 240 tons.

According to the problem, the amount of grain in both elevators is equal after this operation. Therefore, we can set up the following equation:

(x - 960) = (x/3) + 240

Let's solve this equation to find the initial amount of grain in each elevator.

Solving the Equation

To solve the equation, we can start by simplifying it:

x - 960 = x/3 + 240

Multiplying both sides of the equation by 3 to eliminate the fraction:

3(x - 960) = x + 720

Expanding the brackets:

3x - 2880 = x + 720

Moving all the x terms to one side and the constant terms to the other side:

3x - x = 720 + 2880

Simplifying:

2x = 3600

Dividing both sides by 2:

x = 1800

Therefore, the initial amount of grain in the first elevator is 1800 tons. Since the second elevator has three times less grain, the initial amount of grain in the second elevator is 1800/3 = 600 tons.

Answer

The initial amount of grain in the first elevator was 1800 tons, and the initial amount of grain in the second elevator was 600 tons.