Question

10. На першій полиці було у 7 разів більше книжок,ніж на другій. Коли з першої полиці забрали 20(книжок), а на другу поклали 22(книги),то на обох полицях стало порiвно книжок. Скільки книжок було на кожній полиці спочатку?​

Answer 1

Нехай на другій полиці лежало х книжок, тоді на першій – 7х. Коли з першої полиці забрали 20 книжок, то стало 7х-20, а на другу поклали 22 книги – х+22. Після цього на полицях стало порівну книг, значить — 7х-20=х+22
7х-х=22+20
6х=42
х=7
На другій полиці спочатку було 7 книг, а на першій — 7•7=49 (книг).
Відповідь: 49 і 7 книг

Answer 2

Problem Analysis

We are given that there were 7 times more books on the first shelf than on the second shelf. After taking 20 books from the first shelf and adding 22 books to the second shelf, the number of books on both shelves became equal. We need to find the initial number of books on each shelf.

Solution

Let's assume the number of books on the second shelf is x. According to the problem, the number of books on the first shelf is 7 times more than x, which is 7x.

After taking 20 books from the first shelf, the number of books on the first shelf becomes 7x - 20. After adding 22 books to the second shelf, the number of books on the second shelf becomes x + 22.

According to the problem, the number of books on both shelves became equal. So we can set up the equation:

7x - 20 = x + 22

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

7x - x = 22 + 20 6x = 42 x = 42 / 6 x = 7

So the initial number of books on the second shelf was 7.

To find the initial number of books on the first shelf, we can substitute the value of x into the equation:

7x = 7 * 7 = 49

Therefore, there were 49 books on the first shelf initially and 7 books on the second shelf initially.

Answer: There were 49 books on the first shelf and 7 books on the second shelf initially.