Question

У трьх кошиках було 60 кг яблук. Коли з одного кошика переклали у другий 3 кг, то в усіх кошиках яблук стало порівну. Скільки кг яблук було у кожному кошику спочатку?

Answer 1

60-40=20(кг)  
38-20=18(кг) 
40-18=22(кг) 

Answer 2

Problem Analysis

We are given three baskets of apples with a total weight of 60 kg. When 3 kg of apples are transferred from one basket to another, the apples are then distributed equally among all three baskets. We need to determine the initial weight of apples in each basket.

Solution

Let's assume the initial weights of the three baskets are x, y, and z kg respectively.

According to the given information, the total weight of the apples in the three baskets is 60 kg. Therefore, we have the equation:

x + y + z = 60 (Equation 1)

When 3 kg of apples are transferred from one basket to another, the apples are then distributed equally among all three baskets. This means that each basket now has (x - 3), (y + 3), and (z) kg of apples respectively.

According to the second condition, the apples are distributed equally among all three baskets. Therefore, we have the equation:

(x - 3) = (y + 3) = (z) (Equation 2)

We can solve these two equations simultaneously to find the initial weights of the apples in each basket.

Solving the Equations

Let's solve the equations using the substitution method.

From Equation 2, we have:

x - 3 = y + 3 (Equation 3)

Rearranging Equation 3, we get:

x - y = 6 (Equation 4)

Substituting Equation 4 into Equation 1, we have:

(x - y) + z = 60

Substituting the value of (x - y) from Equation 4, we get:

6 + z = 60

Simplifying, we find:

z = 60 - 6 z = 54 (Equation 5)

Substituting the value of z from Equation 5 into Equation 2, we have:

(x - 3) = (y + 3) = 54

Simplifying, we find:

x - 3 = y + 3 = 54

Adding 3 to both sides of the equation, we get:

x = y + 6 = 57 (Equation 6)

Substituting the value of x from Equation 6 into Equation 1, we have:

(y + 6) + y + 54 = 60

Simplifying, we find:

2y + 60 = 60

Subtracting 60 from both sides of the equation, we get:

2y = 0

Dividing both sides of the equation by 2, we find:

y = 0

Substituting the value of y = 0 into Equation 6, we have:

x = 0 + 6 = 6

Substituting the values of x = 6 and y = 0 into Equation 5, we have:

z = 54

Therefore, the initial weights of the apples in each basket were 6 kg, 0 kg, and 54 kg respectively.

Answer

The initial weights of the apples in each basket were 6 kg, 0 kg, and 54 kg respectively.