Question

4. В одном шкафу было в 5 раз меньше книг, чем в другом. Когда в первый шкаф положили 10 книг, а из второго взяли 30, то в обоих шкафах книг стало поровну. Сколько книг было в каждом шкафу? [3]​

Answer 1

Ответ:

Обозначим количество книг в первом шкафу за х, тогда во втором было 5х.

В первый положили 10 книг - x+10

Из второго взяли 30 книг - 5х-30

Т.к в шкафах стало книг поровну, то мы можем приравнять эти выражения и получить уравнение

x+10=5x-30

-4x=-30-10

-4x= -40 умножаем на -1

4x = 40

x = 10 - книг в первом шкафу

во втором было книг 5х = 5•10 = 50книг

Ответ:10;50

Answer 2

Пусть 1 шкаф будет x, тогда во втором шкафу книг в пять раз больше - 5x

x+10(книг)=5х-30(книг)

x=5x-30-10

x-5x=-40

-4x=-40

x=40/4

x=10

1 шкаф: x=10 книг

2 шкаф: 5x=50 книг

Answer 3

Problem Analysis

We are given two cabinets, and the number of books in one cabinet is 5 times less than the number of books in the other cabinet. After adding 10 books to the first cabinet and removing 30 books from the second cabinet, the number of books in both cabinets becomes equal. We need to find the number of books in each cabinet.

Solution

Let's assume the number of books in the first cabinet is x. According to the problem, the number of books in the second cabinet is 5 times greater than the number of books in the first cabinet, so the number of books in the second cabinet is 5x.

After adding 10 books to the first cabinet, the number of books becomes x + 10. After removing 30 books from the second cabinet, the number of books becomes 5x - 30.

According to the problem, the number of books in both cabinets becomes equal. So we can set up the following equation:

x + 10 = 5x - 30

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

x + 10 = 5x - 30

4x = 40

x = 10

So the number of books in the first cabinet is 10, and the number of books in the second cabinet is 5 times greater, which is 50.

Answer

There are 10 books in the first cabinet and 50 books in the second cabinet.