Question

Пожалуйста , помогите решить задачу по математике : На первой полке в 8 раз больше книг, чем на второй. если с первой полки снять 4 книги, а на вторую поставить 10 , то книг на полках станет поровну . На сколько больше книг было на первой полке , чем на второй.

Answer 1

Решаем по уровнению 8х первая полка, х вторая. 8х потому что в 8 раз больше

8х-4=х+10        а значить  в первой полке 16 книг, а в второй 2. 
8х-х=4+10        16 делить на 2 выходит 8 а значит правильное решение
7х=14               в 1 полке в 14  больне книг чем на второй. (16-2=14)
х=2

Answer 2

Problem Analysis

To solve this math problem, we need to determine the number of books on each shelf before and after the given actions. Let's break down the information provided:

- The number of books on the first shelf is 8 times greater than the number of books on the second shelf. - After removing 4 books from the first shelf and adding 10 books to the second shelf, the number of books on both shelves becomes equal.

We need to find the difference in the number of books between the first and second shelves before the actions were taken.

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 8 times greater than x, which means it is equal to 8x.

After removing 4 books from the first shelf, the number of books on the first shelf becomes 8x - 4. After adding 10 books to the second shelf, the number of books on the second shelf becomes x + 10.

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

8x - 4 = x + 10

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

8x - x = 10 + 4

7x = 14

x = 2

So, the number of books on the second shelf before the actions were taken is 2.

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

8x = 8 * 2 = 16

Therefore, the number of books on the first shelf before the actions were taken is 16.

Answer

The number of books on the first shelf was 16 more than the number of books on the second shelf before the actions were taken.