Question

Даю 50 баллов На двух полках 36 книг. Если с одной полки переложить на другую 4 книги, то на первой полке станет книг в два раза меньше , чем на второй. Сколько книг было на каждой полке первоначально?

Answer 1

Ответ:

$16$ и $20$

Пошаговое объяснение:

Решим задачу, составив систему уравнений.

Пусть $x$ (книг) было на первой полке, и $y$ (книг) на второй полке. Вместе на двух полках $x+y=36$ книг. Если с одной полки переложить на другую, то на первой полке станет книг в 2 раза меньше, чем во второй - получим уравнение $2\cdot(x-4)=y+4$

$\displaystyle \left \{ {{x+y=36} \atop {2\cdot(x-4)=y+4}} \right.$

Решим эту систему

$\displaystyle \left \{ {{y=36-x} \atop {2x-8=y+4}} \right.$

$\displaystyle \left \{ {{y=36-x} \atop {2x-8=36-x+4}} \right.$

$\displaystyle \left \{ {{y=36-x} \atop {3x=48}} \right.$

$\displaystyle \left \{ {{y=36-x} \atop {x=16}} \right.$

$\displaystyle \left \{ {{y=20} \atop {x=16}} \right.$

Это ответ.

Проверка

$20+16=36$

$16-4=12=(20+4):2$

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 will be half the number of books on the second shelf. We need to determine the initial number of books on each shelf.

Solution

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

According to the given information, if we move 4 books from the first shelf to the second shelf, the number of books on the first shelf will be half the number of books on the second shelf. Mathematically, we can represent this as:

x - 4 = (y + 4) / 2

Simplifying this equation, we get:

2x - 8 = y + 4

Rearranging the equation, we have:

2x - y = 12 ---(Equation 1)

We also know that the total number of books on both shelves is 36. Mathematically, we can represent this as:

x + y = 36 ---(Equation 2)

We now have a system of two equations (Equation 1 and Equation 2) that we can solve to find the values of x and y.

Solving the System of Equations

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

Multiplying Equation 2 by 2, we get:

2(x + y) = 2(36)

Simplifying, we have:

2x + 2y = 72 ---(Equation 3)

Now, subtracting Equation 1 from Equation 3, we get:

(2x + 2y) - (2x - y) = 72 - 12

Simplifying, we have:

3y = 60

Dividing both sides by 3, we get:

y = 20

Substituting the value of y into Equation 2, we can find the value of x:

x + 20 = 36

Simplifying, we have:

x = 16

Therefore, the initial number of books on the first shelf was 16, and the initial number of books on the second shelf was 20.

Answer

The initial number of books on each shelf was: - First shelf: 16 books - Second shelf: 20 books

Please let me know if you need any further clarification.