Question

8. На першій полиці стояло в 2 рази більше книжок, ніж на другій. Після того, як з першої полиці взяли 1 книгу, а на другу поставили 5 книг, на обохполицях книг стало порівну. Скільки книг стояло на першій полиці спочатку?​

Answer 1

Ответ:

12 книг

Пошаговое объяснение:

На 1 полке стояло 2x книг, а на 2 полке x книг.

С 1 полки убрали 1 книгу, стало 2x - 1 книг.

На 2 полку поставили 5 книг, стало x + 5 книг.

И книг стало поровну на обеих полках.

2x - 1 = x + 5

2x - x = 5 + 1

x = 6 книг было на 2 полке сначала.

2x = 12 книг было на 1 полке сначала.

Answer 2

Solution:

Let's denote the initial number of books on the first shelf as x and on the second shelf as y.

According to the given information: 1. The number of books on the first shelf was twice as many as on the second shelf, so we have the equation: x = 2y. 2. After taking 1 book from the first shelf and adding 5 books to the second shelf, the number of books became equal on both shelves, so we have the equation: (x - 1) = (y + 5).

We can solve these equations to find the initial number of books on the first shelf.

Calculations:

Using the equation x = 2y, we can substitute the value of x in the second equation: (2y - 1) = (y + 5).

Solving for y: 2y - 1 = y + 5 2y - y = 5 + 1 y = 6

Now, we can find the initial number of books on the first shelf using the equation x = 2y: x = 2 * 6 x = 12

So, there were 12 books on the first shelf initially.

Therefore, the initial number of books on the first shelf was 12.