Question

В книжном шкафу на трёх полках стояли 103 книги . После того, как с одной полки на другую переставили 4 книги, а с третьей убрали 7 книг, книг на полках стало поровну. Сколько книг было на каждой полке в начале?

Answer 1

На 1 полке было 36 книг, на 2- 28, а на 3- 39.
36+28+39=103. 36-4=32 28+4=32 39-7=32.

Answer 2

Problem Analysis

We are given that there were 103 books on three shelves in a bookcase. After moving 4 books from one shelf to another and removing 7 books from the third shelf, the number of books on each shelf became equal. We need to determine how many books were initially on each shelf.

Solution

Let's assume that there were x books on the first shelf, y books on the second shelf, and z books on the third shelf.

According to the given information, we can form the following equations:

1. The total number of books on the three shelves is 103: - x + y + z = 103

2. After moving 4 books from one shelf to another and removing 7 books from the third shelf, the number of books on each shelf became equal: - (x - 4) = (y + 4) = (z - 7)

To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method.

From equation 2, we have: - x - 4 = y + 4 - x = y + 8

Substituting this value of x in equation 1, we get: - (y + 8) + y + z = 103 - 2y + z = 95

Now, we have two equations: - 2y + z = 95 - x = y + 8

We can solve these equations to find the values of x, y, and z.

Calculation

Let's solve the system of equations:

From equation 2, we have: - x = y + 8

Substituting this value of x in equation 1, we get: - (y + 8) + y + z = 103 - 2y + z = 95

Now, we have two equations: - 2y + z = 95 - x = y + 8

To find the values of x, y, and z, we can use trial and error or substitution. Let's try trial and error:

Let's assume y = 30. Substituting this value in the equation 2, we get: - x = 30 + 8 - x = 38

Substituting the values of x and y in equation 1, we get: - 38 + 30 + z = 103 - z = 103 - 38 - 30 - z = 35

Therefore, there were 38 books on the first shelf, 30 books on the second shelf, and 35 books on the third shelf in the beginning.

Answer

There were 38 books on the first shelf, 30 books on the second shelf, and 35 books on the third shelf in the beginning.