Question

На двух полках стоят 36 книг. Если с одной полки переложить на вторую 4 книги то на первой полке станет книг в 2 раза меньше чем на второй. Сколько книг было на каждой полке?

Answer 1

Ответ:

16 книг было на первой полке

20 книг было на второй полке

Пошаговое объяснение:

Пусть х книг было на первой полке, тогда 36-х книг на второй полке

Если с первой полки переложить на вторую 4 книги, то на первой полке станет книг в 2 раза меньше, чем на второй.

Составим уравнение:

2(х - 4) = 36 - х + 4

2х - 8 = 40 - х

2х + х = 40 + 8  

3х = 48   х = 48/3     х = 16 книг было на первой полке

36 - 16 = 20 книг было на второй полке

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16 - 4 = 12 книг осталось на первой полке

20 + 4 = 24 книги стало на второй полке

24/12 = 2 - на первой полке стало книг в 2 раза меньше чем на второй

Answer 2

Problem Analysis

We are given that there are 36 books on two shelves. If we move 4 books from one shelf to the other, the number of books on the first shelf becomes half the number of books on the second shelf. We need to determine the number of books on each shelf.

Solution

Let's assume the number of books on the first shelf is x and the number of books on the second shelf is y.

According to the given information, we have the following equations: 1. x + y = 36 (since there are 36 books in total) 2. x - 4 = (y + 4) / 2 (since the number of books on the first shelf becomes half the number of books on the second shelf after moving 4 books)

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

Solving the Equations

Let's solve the equations using substitution or elimination method.

From equation 1, we have: x = 36 - y

Substituting this value of x in equation 2, we get: 36 - y - 4 = (y + 4) / 2

Simplifying the equation: 32 - y = (y + 4) / 2

Multiplying both sides of the equation by 2 to eliminate the fraction: 64 - 2y = y + 4

Bringing all the terms involving y to one side of the equation: 3y = 60

Dividing both sides of the equation by 3: y = 20

Substituting the value of y in equation 1 to find x: x = 36 - 20 x = 16

Answer

There were 16 books on the first shelf and 20 books on the second shelf.

Note: The solution provided above is based on the given information and the assumption that the number of books on each shelf is a whole number.