Question

Розв'язати задачу рівнянням: На одній полиці утричі більше книжок ніж на другій після того, як з першої полиці переклали на другу 15книг, то на полицях книг стало порівну. Скільки книг було на кожній полиці спочатку?

Answer 1

х - було на другій полиці 5х - було на першій 5х-12=х+12 5х-х=12+12 4х=24 х=24:4 х=6 (книг) було на другий 5*6=30 (книг) на першій Відповідь: на першій полиці було 30 книг, на другий 6 книг

Answer 2

Problem Analysis

To solve this problem, we need to find the number of books on each shelf initially. Let's assume that the number of books on the first shelf is x, and the number of books on the second shelf is y.

According to the problem, after transferring 15 books from the first shelf to the second shelf, the number of books on both shelves becomes equal.

Solution

To solve the problem, we can set up the following equation:

x - 15 = y + 15

This equation represents the fact that after transferring 15 books from the first shelf to the second shelf, the number of books on both shelves becomes equal.

Now, let's solve this equation to find the values of x and y.

x - 15 = y + 15

x - y = 30

From this equation, we can see that the difference between the number of books on the first shelf and the second shelf is 30.

To find the values of x and y, we need to consider that there are more books on the first shelf than on the second shelf.

Let's assume that the number of books on the first shelf is x = y + 30.

Now, we can substitute this value of x into the equation x - 15 = y + 15:

y + 30 - 15 = y + 15

y + 15 = y + 15

By subtracting y from both sides of the equation, we get:

15 = 15

This equation is true for any value of y. Therefore, there are infinitely many solutions to this problem.

In conclusion, there are infinitely many possible initial configurations of books on the shelves that satisfy the given conditions.