Question

В двух книжных шкафах было 1536 книг. Когда из одного взяли 156 книг, а из другого в 3 раза больше, то книг в шкафу стало поровну. Сколько книг было в каждом шкафу первоначально?

Answer 1

Пусть х книг было в первом шкафу, тогда во втором (1536-х) книг
из первого взяли 156 стало х-156, из второго 156·3=468, стало (1536-х)-468, т.к. книг стало поровну составим уравнение
х-156=(1536-х)-468
2х=1224
х= 612
1536-612= 924
ответ 612 и 924

Answer 2

1)1536-156=1380. 2)156•3=468. 3)1380-468=912. 4)912:2=456. 5)456+156=612. 6)456+468=924. Ответ : первый шкаф -612 второй шкаф - 924.

Answer 3

Problem Analysis

We are given that there were initially 1536 books in two bookcases. From one bookcase, 156 books were taken, and from the other bookcase, three times as many books were taken. After this, the number of books in the two bookcases became equal. We need to find the initial number of books in each bookcase.

Solution

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

According to the given information, we can form the following equations:

1. The total number of books in the first bookcase after some books were taken: x - 156 2. The total number of books in the second bookcase after three times as many books were taken: y - (3 * 156)

Since the number of books in the two bookcases became equal, we can set up the following equation:

x - 156 = y - (3 * 156)

Simplifying the equation:

x - 156 = y - 468

Rearranging the equation:

x - y = -312 ---(Equation 1)

We also know that the total number of books in the two bookcases initially was 1536:

x + y = 1536 ---(Equation 2)

Now, we 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 the method of substitution or elimination. Let's use the elimination method.

Adding Equation 1 and Equation 2, we get:

(x - y) + (x + y) = -312 + 1536

Simplifying the equation:

2x = 1224

Dividing both sides by 2:

x = 612

Substituting the value of x into Equation 2:

612 + y = 1536

Simplifying the equation:

y = 924

Answer

The initial number of books in the first bookcase was 612, and the initial number of books in the second bookcase was 924.

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