Question

В одной пачке было в 2,5 раза больше тетрадей, чем в другой. Когда из второй пачки переложили в первую 15 тетрадей, то во второй пачке стало в 3 раза меньше тетрадей, чем впервой. Сколько тетрадей было в каждой пачке первоначально?

Answer 1

Ответ:

Удачи!

Пошаговое объяснение:

1 пачка - 2.5х

2 пачка- х

1 пачка - 2.5 х + 15

2 пачка - х - 15

3( x - 15 ) = 2.5x + 15

3x - 45 = 2.5x + 15

0.5x= 60

x=120 тетрадей - 2 пачка

2.5 × 120 = 300 - 1 пачка

Answer 2

Problem Analysis

We are given two packs of notebooks, and the number of notebooks in one pack is 2.5 times greater than the number in the other pack. After transferring 15 notebooks from the second pack to the first pack, the number of notebooks in the second pack becomes three times smaller than the number in the first pack. We need to find 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 in the second pack is y.

According to the given information: 1. The number of notebooks in the first pack is 2.5 times greater than the number in the second pack: x = 2.5y. 2. After transferring 15 notebooks from the second pack to the first pack, the number of notebooks in the second pack becomes three times smaller than the number in the first pack: (y - 15) = (1/3)(x + 15).

We can solve this system of equations to find the values of x and y.

Solving the System of Equations

Let's substitute the value of x from the first equation into the second equation:

(y - 15) = (1/3)(2.5y + 15).

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

Calculations

Expanding the equation:

y - 15 = (1/3)(2.5y + 15).

Multiplying both sides by 3 to eliminate the fraction:

3(y - 15) = 2.5y + 15.

Expanding the equation:

3y - 45 = 2.5y + 15.

Subtracting 2.5y from both sides:

0.5y - 45 = 15.

Adding 45 to both sides:

0.5y = 60.

Dividing both sides by 0.5:

y = 120.

Now, we can substitute the value of y back into the first equation to find the value of x:

x = 2.5y = 2.5 * 120 = 300.

Answer

The initial number of notebooks in the first pack was 300, and in the second pack was 120.