Question

На двух полках стояло 12 книг.Когда с первой полки на вторую переставили столько книг,сколько до этого стояло на второй полке ,то книг на полках стало поровну.Определите ,сколько книг первоначально стояло на каждой полке.

Answer 1

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Answer 2

Problem Analysis

We are given that there are 12 books on two shelves. When we move some books from the first shelf to the second shelf, the number of books on each shelf becomes equal. We need to determine the initial number of books on each shelf.

Solution

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

According to the problem, when we move some books from the first shelf to the second shelf, the number of books on each shelf becomes equal. This can be expressed as the equation:

x - n = y + n, where n represents the number of books moved from the first shelf to the second shelf.

Simplifying the equation, we get:

2n = x - y

We also know that the total number of books on both shelves is 12. So we have another equation:

x + y = 12

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

Let's solve the equations:

2n = x - y (Equation 1)

x + y = 12 (Equation 2)

To eliminate y, we can add Equation 1 and Equation 2:

(2n) + (x + y) = (x - y) + (x + y)

Simplifying, we get:

2n + 12 = 2x

Rearranging the equation, we get:

2x - 2n = 12

Dividing both sides by 2, we get:

x - n = 6

Now we have a new equation:

x - n = 6 (Equation 3)

We can solve Equation 3 and Equation 2 simultaneously to find the values of x and n.

Let's solve the equations:

x - n = 6 (Equation 3)

x + y = 12 (Equation 2)

Adding Equation 3 and Equation 2, we get:

(x - n) + (x + y) = 6 + 12

Simplifying, we get:

2x + y = 18

Now we have a new equation:

2x + y = 18 (Equation 4)

We can solve Equation 4 and Equation 2 simultaneously to find the values of x and y.

Let's solve the equations:

2x + y = 18 (Equation 4)

x + y = 12 (Equation 2)

Subtracting Equation 2 from Equation 4, we get:

(2x + y) - (x + y) = 18 - 12

Simplifying, we get:

x = 6

Now that we have the value of x, we can substitute it into Equation 2 to find the value of y:

6 + y = 12

Simplifying, we get:

y = 6

Therefore, the initial number of books on each shelf was 6.

Answer

The initial number of books on each shelf was 6.