Question

На первой полке стояло в 3 раза больше книг, чем на второй. Когда с первой полки сняли 8 книг, а на вторую поставили 14 книг, то на полках книг стало поровну. Сколько книг было на каждой полке первоначально? ПОЖАЛУЙСТА ПОМОГИТЕ СРОЧНО!

Answer 1

Пусть х книг на 2ой полке, на 1ой 3х. После изменений (3х-8) на 1ой полке, а на 2ой (х+14).
3х-8=х+14
3х-х=14+8
2х=22
х=11 ( на 2 полке было)
3х=3×11=33 на первой было

Answer 2

Problem Analysis

We are given that there are three times as many books on the first shelf as on the second shelf. When 8 books are removed from the first shelf and 14 books are added to the second shelf, the number of books on each shelf becomes equal. We need to determine 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 given information, the number of books on the first shelf is three times that of the second shelf, so it would be 3x.

When 8 books are removed from the first shelf, the number of books on the first shelf becomes 3x - 8. Similarly, when 14 books are added to the second shelf, the number of books on the second shelf becomes x + 14.

According to the problem, the number of books on each shelf becomes equal after these changes. Therefore, we can set up the following equation:

3x - 8 = x + 14

Now, let's solve this equation to find the value of x.

3x - 8 = x + 14

2x = 22

x = 11

So, the initial number of books on the second shelf is 11, and the initial number of books on the first shelf is three times that, which is 33.

Therefore, there were initially 33 books on the first shelf and 11 books on the second shelf.

Answer

There were initially 33 books on the first shelf and 11 books on the second shelf.