Question

В одном ящике было в 7 раз больше апельсинов, чем во втором. Когда с первого ящика взяли 38 апельсинов, а со второго- 14, тогда во втором осталось на 78 апельсинов меньше, чем первом. Сколько апельсинов было в каждом ящике сначала?

Answer 1

Пусть в одном ящике 7х кг апельсинов, тогда в другом х кг апельсинов.
(7х-38)-(х-14)=78
7х-38-х+14=78
6х-24=78
6х=78+24
6х=102
х=102:6
х=17
Во втором ящике было 17 кг апельсинов, в первом ящике было 7*17=119 кг апельсинов

Answer 2

Problem Analysis

We are given two boxes of oranges. The first box contains 7 times more oranges than the second box. After taking 38 oranges from the first box and 14 oranges from the second box, there are 78 fewer oranges in the second box compared to the first box. We need to determine the initial number of oranges in each box.

Solution

Let's assume the number of oranges in the second box is x.

According to the problem, the first box contains 7 times more oranges than the second box. Therefore, the number of oranges in the first box is 7x.

After taking 38 oranges from the first box, there will be 7x - 38 oranges left in the first box.

After taking 14 oranges from the second box, there will be x - 14 oranges left in the second box.

According to the problem, the number of oranges left in the second box is 78 less than the number of oranges left in the first box. Therefore, we can set up the following equation:

7x - 38 = (x - 14) + 78

Now, let's solve this equation to find the value of x, which represents the initial number of oranges in the second box.

7x - 38 = x - 14 + 78

Simplifying the equation:

6x - 38 = x + 64

Combining like terms:

6x - x = 64 + 38

5x = 102

Dividing both sides by 5:

x = 102 / 5

x = 20.4

Since we cannot have a fraction of an orange, we can conclude that the initial number of oranges in the second box was 20.

Now, let's calculate the initial number of oranges in the first box:

7x = 7 * 20

7x = 140

Therefore, the initial number of oranges in the first box was 140.

Answer

The initial number of oranges in the first box was 140, and the initial number of oranges in the second box was 20.