Question

Решите задачу на одном овощехранилище было втрое больше картофеля чем на другом.С первого хранилища вывезли 450 т картофеля, а на второе привезли 120т, после чего на обоих овощехранилищах стало картофеля поровну. Сколько тонн картофеля было на каждом овощехранилище первоначально?

Answer 1

Пусть Хт - на одном овощехранилище, тогда на другом - 3Хт

3Х -450 =Х +120

3Х -Х=120+450

2Х =570

Х = 570:2

Х = 285 т - на одном овощехранилище                          285 х 3 =855т - на другом

Answer 2

Problem Analysis

To solve this problem, we need to determine the initial amount of potatoes in each vegetable storage. We are given that one storage had three times more potatoes than the other. Additionally, we know that 450 tons of potatoes were taken from the first storage, while 120 tons were brought to the second storage. After these transactions, the amount of potatoes in both storages became equal.

Solution

Let's assume that the initial amount of potatoes in the first storage was x tons. According to the problem, the second storage had three times less potatoes, so its initial amount was x/3 tons.

After 450 tons were taken from the first storage, the remaining amount of potatoes in the first storage is x - 450 tons. Similarly, after 120 tons were brought to the second storage, the total amount of potatoes in the second storage is x/3 + 120 tons.

Since the amount of potatoes in both storages became equal, we can set up the following equation:

x - 450 = x/3 + 120

To solve this equation, we can start by multiplying both sides by 3 to eliminate the fraction:

3(x - 450) = x + 360

Expanding the equation:

3x - 1350 = x + 360

Next, we can simplify the equation by combining like terms:

3x - x = 360 + 1350

Simplifying further:

2x = 1710

Finally, we can solve for x by dividing both sides by 2:

x = 855

Therefore, the initial amount of potatoes in the first storage was 855 tons, and the initial amount in the second storage was 855/3 = 285 tons.

Answer

The initial amount of potatoes in each vegetable storage was: - First storage: 855 tons - Second storage: 285 tons

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