Question

У 3х ящиках є 58.5 кг.яблук у 1му та 2му разом 2/3 усіх яблук а в2му і 3му 80% усіх яблук.Скільки кг яблук у кожному ящику??

Answer 1

Problem Analysis

We are given three boxes with a total weight of 58.5 kg of apples. The first and second boxes together contain 2/3 of all the apples, while the second and third boxes contain 80% of all the apples. We need to determine the weight of apples in each box.

Solution

Let's assume the weights of the apples in the first, second, and third boxes are x, y, and z kilograms, respectively.

From the given information, we can set up the following equations:

Equation 1: x + y + z = 58.5 (since the total weight of all three boxes is 58.5 kg)

Equation 2: x + y = (2/3) * (x + y + z) (since the first and second boxes together contain 2/3 of all the apples)

Equation 3: y + z = 0.8 * (x + y + z) (since the second and third boxes contain 80% of all the apples)

We can solve these equations to find the values of x, y, and z.

Solving the Equations

Let's start by simplifying Equation 2 and Equation 3:

Equation 2: x + y = (2/3) * (x + y + z) => 3x + 3y = 2x + 2y + 2z => x + y = 2z

Equation 3: y + z = 0.8 * (x + y + z) => y + z = 0.8x + 0.8y + 0.8z => 0.2y + 0.2z = 0.8x

Now, let's substitute the value of (x + y) from Equation 2 into Equation 3:

0.2y + 0.2z = 0.8x => 0.2y + 0.2z = 0.8(2z) => 0.2y + 0.2z = 1.6z => 0.2y = 1.4z => y = 7z

Now, let's substitute the value of y into Equation 2:

x + y = 2z => x + 7z = 2z => x = -5z

Since the weights of the apples cannot be negative, we can conclude that z = 0.

Substituting z = 0 into Equation 2 and Equation 3, we get:

x + y = 2z => x + y = 2(0) => x + y = 0

y + z = 0.8 * (x + y + z) => y + 0 = 0.8 * (x + y + 0) => y = 0

Therefore, the weight of apples in each box is 0 kg.

Answer

There are 0 kg of apples in each box.

Please let me know if you need any further assistance!