Question

У двох кошиках було 24 кг груш. Коли з одного кошика переклали в другий 4/7 маси груш, які були в першому, то маса груш у другому кошику стала вдвічі більшою за масу груш, що залишилися в першому. Скільки кілограмів груш було в кожному кошику спочатку?

Answer 1

Ответ:

Пошаговое объяснение:

Нехай у одному кошику було -х кг груш , тоді у другому кошику було (24-х) кг груш, коли у другий переклали 4/7маси , то маса стала більшою вдвічі (х-4/7х)*2

(х-4/7х)*2=24-х+4/7х

6/7х=24-4/7х           (24=168/7)

6/7х=168/7-4/7х  помножимо обидві сторони на 7

6х=168 - 3х

9х=168

х= 168/9

х=18 2/3 кг груш у першому кошику

24- 18 2/3 = 5 1/3 кг груш у другому кошику

Answer 2

Problem Analysis

We are given that there were 24 kg of pears in two baskets. When 4/7 of the pears from one basket were transferred to the other basket, the mass of pears in the second basket became twice the mass of the pears remaining in the first basket. We need to determine the initial masses of pears in each basket.

Solution

Let's assume that the initial mass of pears in the first basket is x kg. Therefore, the initial mass of pears in the second basket is 24 - x kg.

According to the problem, when 4/7 of the pears from the first basket are transferred to the second basket, the mass of pears in the second basket becomes twice the mass of the pears remaining in the first basket.

Mathematically, we can express this as:

(24 - x) + (4/7)x = 2(x - (4/7)x)

Simplifying the equation:

(24 - x) + (4/7)x = 2(3/7)x

Multiplying both sides of the equation by 7 to eliminate the fraction:

7(24 - x) + 4x = 6x - (8/7)x

Expanding and simplifying:

168 - 7x + 4x = 6x - (8/7)x

Combining like terms:

168 - 3x = (42/7)x - (8/7)x

Simplifying the right side:

168 - 3x = (34/7)x

Multiplying both sides of the equation by 7 to eliminate the fraction:

7(168 - 3x) = 34x

Expanding:

1176 - 21x = 34x

Adding 21x to both sides:

1176 = 55x

Dividing both sides by 55:

x = 1176/55

Evaluating the value of x:

x ≈ 21.38

Therefore, the initial mass of pears in the first basket is approximately 21.38 kg. The initial mass of pears in the second basket can be calculated as:

24 - x = 24 - 21.38 ≈ 2.62

Therefore, the initial mass of pears in the second basket is approximately 2.62 kg.

Answer

The initial mass of pears in the first basket was approximately 21.38 kg, and the initial mass of pears in the second basket was approximately 2.62 kg.