Question

Решите задачу с помощью уравнения. В книжном шкафу на верхней полке было в 3 раза больше книг, чем на нижней. После того, как на нижнюю полку добавили 6 книг, а с верхней взяли 2 книги, на обеих полках книг стало поровну. Сколько книг было на нижней полке?

Answer 1

Ответ:

4

Пошаговое объяснение:

Составляем уровнение:

х + 6 = 3х - 2

-2х = -8

х = 4

Answer 2

Problem Analysis

To solve this problem using an equation, let's assume the number of books on the bottom shelf is represented by the variable x. According to the problem, the number of books on the top shelf is 3 times greater than the number on the bottom shelf. After adding 6 books to the bottom shelf and taking away 2 books from the top shelf, the number of books on both shelves becomes equal. We need to find the value of x, which represents the number of books on the bottom shelf.

Solution

Let's break down the information given in the problem and solve it step by step:

1. The number of books on the top shelf is 3 times greater than the number on the bottom shelf. This can be represented as: - Number of books on the top shelf = 3 * Number of books on the bottom shelf - Number of books on the top shelf = 3x

2. After adding 6 books to the bottom shelf and taking away 2 books from the top shelf, the number of books on both shelves becomes equal. This can be represented as: - Number of books on the bottom shelf + 6 = Number of books on the top shelf - 2 - x + 6 = 3x - 2

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

x + 6 = 3x - 2 6 + 2 = 3x - x 8 = 2x x = 4

Answer

Therefore, there were 4 books on the bottom shelf.