Question

Домашняя работа. 9. Если Алена переложит с первой полки 8 книг на вторую, то на второй полке станет в 5 раз больше книг, чем на первой. Сколько книг было первоначально на каждой полке, если всего 60 книг? 10 раб an Cronto

Answer 1

Ответ:

На первой полке - 18 книг , на второй - 42 книги

Пошаговое объяснение:

Пусть на первой полке было х книг , тогда на второй полке было ( 60-х) книг. Когда Алена переложила с первой полки на вторую 8 книг , то на первой полке стало : (х - 8) книг , а на второй 60 - х + 8 = 68 - х книг и это в 5 раз больше , чем на первой . Умножим количество книг на первой полке на 5 и приравняем к количеству книг на второй полке , получим равность :

5( х-8) = 68 - х

5х - 40 = 68 - х

5х + х = 68 + 40

6х = 108

х = 108 : 6

х = 18 книг было изначально на первой полке

60 - 18 = 42 книги было изначально на второй полке

Answer 2

Problem Analysis

We are given that if Alena moves 8 books from the first shelf to the second, the second shelf will have 5 times more books than the first shelf. We need to determine the initial number of books on each shelf, given that there are a total of 60 books.

Solution

Let's assume that the initial number of books on the first shelf is x. According to the given information, if Alena moves 8 books from the first shelf to the second, the second shelf will have 5 times more books than the first shelf. This can be expressed as:

Number of books on the second shelf = 5 * Number of books on the first shelf

After moving 8 books from the first shelf to the second, the number of books on the first shelf will be x - 8. So, we can write the equation:

5 * (x - 8) = x

Now, we can solve this equation to find the value of x, which represents the initial number of books on the first shelf.

Calculation

Let's solve the equation:

5 * (x - 8) = x

Expanding the equation:

5x - 40 = x

Bringing all the x terms to one side:

5x - x = 40

4x = 40

Dividing both sides by 4:

x = 10

So, the initial number of books on the first shelf is 10.

Now, we can calculate the initial number of books on the second shelf:

Number of books on the second shelf = 5 * Number of books on the first shelf

Number of books on the second shelf = 5 * 10 = 50

Therefore, the initial number of books on the second shelf is 50.

Answer

The initial number of books on the first shelf is 10, and the initial number of books on the second shelf is 50.