Question

На шоколадную фабрику привезли 2 ящика какао бобов. В первом ящике было 10,5 раз больше какао бобов чем во втором.После того как из первого ящика взяли 16 кг, а во второй добавили 22 кг, какао бобов стало поровну. Сколько какао бобов было первоначально в каждом ящике?

Answer 1

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Answer 2

Problem Analysis

We are given that 2 boxes of cocoa beans were delivered to a chocolate factory. The first box contains 10.5 times more cocoa beans than the second box. After taking out 16 kg from the first box and adding 22 kg to the second box, the number of cocoa beans became equal in both boxes. We need to find the initial number of cocoa beans in each box.

Solution

Let's assume the initial number of cocoa beans in the second box is x. According to the problem, the first box contains 10.5 times more cocoa beans than the second box, so the number of cocoa beans in the first box is 10.5x.

After taking out 16 kg from the first box, the number of cocoa beans in the first box will be reduced. Let's calculate the new number of cocoa beans in the first box:

New number of cocoa beans in the first box = 10.5x - 16

After adding 22 kg to the second box, the number of cocoa beans in the second box will increase. Let's calculate the new number of cocoa beans in the second box:

New number of cocoa beans in the second box = x + 22

According to the problem, the number of cocoa beans became equal in both boxes. Therefore, we can set up the following equation:

10.5x - 16 = x + 22

Now, let's solve this equation to find the value of x.

Solving the Equation

To solve the equation, we'll simplify it step by step:

10.5x - 16 = x + 22

Subtract x from both sides:

10.5x - x - 16 = 22

Simplify:

9.5x - 16 = 22

Add 16 to both sides:

9.5x = 38

Divide both sides by 9.5:

x = 4

So, the initial number of cocoa beans in the second box was 4.

Finding the Initial Number of Cocoa Beans in the First Box

Now that we know the initial number of cocoa beans in the second box is 4, we can find the initial number of cocoa beans in the first box using the equation:

New number of cocoa beans in the first box = 10.5x - 16

Substituting the value of x:

New number of cocoa beans in the first box = 10.5 * 4 - 16 = 42 - 16 = 26

Therefore, the initial number of cocoa beans in the first box was 26.

Answer

The initial number of cocoa beans in each box was: - First box: 26 - Second box: 4