Question

Решить задачу! На верхней полке в 3 раза больше книг,чем на нижней полке.После того,как с верхней полки сняли 15 книг,а на нижнюю полку положили 11 книг,то книг на обеих полках стало поровну.Сколько книг было на каждой полке первоначально?

Answer 1

3х- на верхней полке
х-на нижней полке
3х-15=х+11
3х-х=11+15
2х=26
х=13 на нижней
   
13*3=39 на верхней

Answer 2

Пусть на нижней полке х книг,тогда на верхней 3х. Если с верхней полки сняли=>3х-15 Если на нижнюю полку положили=>х+11 После этих действий книг стало поровну,тогда между этими выражениями можно поставить знак равенства,и получить уравнение: 1)3х-15=х+11 3х-х=11+15 2х=26 х=26:2 х=13(книг)-было на нижней полке 2)13*3=39(книг)-было на верхней полке

Answer 3

Problem Analysis

Let's break down the information given in the problem: - The number of books on the top shelf is three times the number of books on the bottom shelf. - After removing 15 books from the top shelf and adding 11 books to the bottom 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 bottom shelf is x. According to the problem, the number of books on the top shelf is three times that, so it would be 3x.

After removing 15 books from the top shelf, the number of books on the top shelf becomes 3x - 15. After adding 11 books to the bottom shelf, the number of books on the bottom shelf becomes x + 11.

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

3x - 15 = x + 11

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

Solving the Equation

Let's solve the equation step by step:

3x - 15 = x + 11

First, let's simplify the equation by combining like terms:

3x - x = 11 + 15

Simplifying further:

2x = 26

Now, let's isolate x by dividing both sides of the equation by 2:

x = 26 / 2

Simplifying:

x = 13

So, the initial number of books on the bottom shelf is 13.

Since the number of books on the top shelf is three times that, the initial number of books on the top shelf is:

3x = 3 * 13 = 39

Therefore, there were initially 39 books on the top shelf and 13 books on the bottom shelf.

Answer

The initial number of books on the top shelf was 39, and the initial number of books on the bottom shelf was 13.

Please let me know if you need any further assistance!