Question

На верхней полке в 3 раза больше книг чем на нижней. После того как с верхней сняли 15 книг,а на нижнюю добавили 11 книг, книг на обеих полках стало поровну. Сколько на каждой полке первоначально было?

Answer 1

Пусть х книг на нижней полке,тогда на верхней полке 3х 

3х - 15 = х + 11

3х - х = 11 + 15

2х = 26

х = 13 - нижняя

13*3 = 39 - верхняя 

Answer 2

Initial Situation

Let's denote the number of books on the lower shelf as x. According to the given information, the number of books on the upper shelf is 3 times the number on the lower shelf, so it can be represented as 3x.

Changes in the Number of Books

After 15 books were removed from the upper shelf and 11 books were added to the lower shelf, the number of books on both shelves became equal. This can be expressed as the equation: 3x - 15 = x + 11

Solving for x

To find the initial number of books on each shelf, we can solve the equation: 3x - 15 = x + 11

Subtracting x from both sides gives: 2x - 15 = 11

Adding 15 to both sides gives: 2x = 26

Dividing by 2 gives: x = 13

Calculating the Initial Number of Books

So, the initial number of books on the lower shelf was 13, and the initial number of books on the upper shelf was 3*13 = 39.

Therefore, initially, there were 13 books on the lower shelf and 39 books on the upper shelf.