Question

В одной пачке было в 2,5 раза больше тетрадей, чем в другой. Когда из второй пачке переложили в первую 5 тетрадей, то во второй стало в 3 раза меньше тетрадей, чем в первой. Сколько тетрадей было в каждой пачку первоначально? Если можно объясните как вы делали! Заранее спасибо!

Answer 1

Пусть х (т).во второй,

в первой 2,5 х тетр.
Тогда, переложили и стало:

в первой 2,5х+5

во второй х-5
Получаем уравнение:
2,5х+5=3(х-5)
2,5х+5=3х-15
2,5х-3х=-15-5
-0,5 х = -20
х = 40-во второй
 2,5 * 40 =100( т)- в первой

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

Answer 2

Problem Analysis

We are given two packs of notebooks, and it is stated that one pack contains 2.5 times more notebooks than the other pack. After transferring 5 notebooks from the second pack to the first pack, the number of notebooks in the second pack becomes 3 times less than the number of notebooks in the first pack. We need to determine the initial number of notebooks in each pack.

Solution

Let's assume that the initial number of notebooks in the first pack is x, and the initial number of notebooks in the second pack is y.

According to the given information, we have the following equations:

1. The first pack contains 2.5 times more notebooks than the second pack: x = 2.5y.

2. After transferring 5 notebooks from the second pack to the first pack, the number of notebooks in the second pack becomes 3 times less than the number of notebooks in the first pack: (y - 5) = (x - 5)/3.

To solve this system of equations, we can substitute the value of x from equation 1 into equation 2 and solve for y.

Calculation

Let's substitute x = 2.5y into equation 2:

(y - 5) = ((2.5y) - 5)/3

Now, we can solve this equation to find the value of y.

Solution Steps

1. Simplify the equation: 3(y - 5) = 2.5y - 5 3y - 15 = 2.5y - 5

2. Move all the terms containing y to one side of the equation: 3y - 2.5y = -5 + 15 0.5y = 10

3. Solve for y: y = 10 / 0.5 y = 20

4. Substitute the value of y back into equation 1 to find x: x = 2.5 * 20 x = 50

Answer

The initial number of notebooks in the first pack was 50, and the initial number of notebooks in the second pack was 20.