Question

На одной полке было в 3 раза больше книг , чем на другой . когда с одной полки сняли 8 книг , а на другую положили 32 книги, то на полках стало книг поровну .Сколько книг было на каждой полке первоначально ?

Answer 1

Пусть х - количество книг на одной полке, а 3х - количество книг на другой полке. Тогда 3х - 8 - количество книг на одной полке, когда с неё сняли 8 книг и х + 32 - количество книг на другой полке, когда на неё добавили 32 книги.
3х - 8 = х + 32
3х - х = 32 + 8
2х = 40
х = 40 : 2
х = 20 (книг) - было первоначально на одной полке.
20 · 3 = 60 (книг) - было первоначально на другой полке.
Ответ: 20 и 60 книг.

Answer 2

3х-8=х+32
3х-8=32+8
2х=40
х=40:2
х=20

Answer 3

Problem Analysis

We are given that there are three times as many books on one shelf as there are on the other. When 8 books are removed from one shelf and 32 books are added to the other 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 that the initial number of books on one shelf is x and the initial number of books on the other shelf is y.

According to the given information: 1. There are three times as many books on one shelf as there are on the other: x = 3y. 2. When 8 books are removed from one shelf and 32 books are added to the other shelf, the number of books on each shelf becomes equal: (x - 8) = (y + 32).

We can solve these two equations to find the values of x and y.

Substituting the value of x from the first equation into the second equation: (3y - 8) = (y + 32).

Simplifying the equation: 3y - 8 = y + 32.

Bringing all the terms involving y to one side: 3y - y = 32 + 8.

Simplifying further: 2y = 40.

Dividing both sides by 2: y = 20.

Substituting the value of y back into the first equation: x = 3(20) = 60.

Therefore, the initial number of books on each shelf was 60 and 20 respectively.

Answer

The initial number of books on each shelf was 60 and 20 respectively.