Question

В одной пачке тетрадей в 2,5 раза больше, чем во второй. Когда из второй пачки достали 5 тетрадей и переложили в первую, то во второй пачке стало в 3 раза меньше тетрадей, чем в первой. Сколько было тетрадей в двух пачках первоначально?

Answer 1

Пусть во второй пачке было х тетрадей, тогда в первой - 2,5х.

Когда из второй пачки взяли 5 тетрадей и переложили их в первую, во второй стало (х-5) тетрадей, а в первой (2,5х+5) тетрадей. Составляем уравнение:

$\frac{2,5x+5}{x-5}=3$

Решаем его, получаем х=40, тогда 2,5х=100.

Ответ: в первой пачке - 100 тетрадей, во второй - 40.

Answer 2

Problem Analysis

We are given two packs of notebooks, and the number of notebooks in the first pack is 2.5 times greater than the number in the second pack. After taking out 5 notebooks from the second pack and transferring them to the first pack, the number of notebooks in the second pack becomes 3 times smaller than the number in the first pack. We need to find the initial number of notebooks in both packs.

Solution

Let's assume that the initial number of notebooks in the second pack is x. According to the problem, the number of notebooks in the first pack is 2.5 times greater than the number in the second pack, so the initial number of notebooks in the first pack is 2.5x.

After taking out 5 notebooks from the second pack and transferring them to the first pack, the number of notebooks in the second pack becomes 3 times smaller than the number in the first pack. This can be expressed as:

x - 5 = (2.5x + 5) / 3

To solve this equation, we can simplify it by multiplying both sides by 3:

3(x - 5) = 2.5x + 5

Expanding the equation:

3x - 15 = 2.5x + 5

Combining like terms:

0.5x = 20

Dividing both sides by 0.5:

x = 40

So, the initial number of notebooks in the second pack is 40. Since the number of notebooks in the first pack is 2.5 times greater, the initial number of notebooks in the first pack is:

2.5 * 40 = 100

Therefore, there were initially 40 notebooks in the second pack and 100 notebooks in the first pack.

Answer

There were initially 40 notebooks in the second pack and 100 notebooks in the first pack.