Question

В первом шкафу было в 4 раза меньше книг, чем во втором. Когда в первый шкаф поставили 17 книг, а из второго взяли 25 книг, в шкафах книг стало поровну. Сколько книг было в каждом шкафу сначало?

Answer 1

х книг было в 1 шкафу

4х книг было во 2 шкафу

х + 17 книг стало в 1 шкафу

4х - 25 стало во 2 шкафу.

ПО условию известно, что огда в первый шкаф положили 17 книг,а из второго взяли 25,то в обоих шкафах стало поровну.

4х - 25 = х + 17

4х - х = 17 + 25

3х = 42

х = 14

14 книг было в 1 шкафу

4 * 14 = 56 книг было во 2 шкафу

Answer 2

Problem Analysis

We are given two cabinets, and the number of books in the first cabinet is four times less than the number of books in the second cabinet. After adding 17 books to the first cabinet and removing 25 books from the second cabinet, the number of books in both cabinets becomes equal. We need to find the initial number of books in each cabinet.

Solution

Let's assume the number of books in the second cabinet is x. Then the number of books in the first cabinet is x/4.

After adding 17 books to the first cabinet, the number of books becomes x/4 + 17.

After removing 25 books from the second cabinet, the number of books becomes x - 25.

According to the problem, the number of books in both cabinets becomes equal. So we can set up the following equation:

x/4 + 17 = x - 25

To solve this equation, we can follow these steps:

1. Multiply both sides of the equation by 4 to eliminate the fraction: 4(x/4 + 17) = 4(x - 25) 2. Simplify: x + 68 = 4x - 100 3. Subtract x from both sides: 68 = 3x - 100 4. Add 100 to both sides: 168 = 3x 5. Divide both sides by 3: x = 56

So the initial number of books in the second cabinet is 56.

The number of books in the first cabinet is four times less than the number of books in the second cabinet, so it is 56/4 = 14.

Therefore, there were initially 14 books in the first cabinet and 56 books in the second cabinet.

Answer

There were initially 14 books in the first cabinet and 56 books in the second cabinet.