Question

У двох кошиках було 60 яблук. Після того як з першого забрали у другий 6 яблук,, то у другому кошику стало у 2 рази більше яблук, ніж у першому. Скільки яблук було спочатку у кожному кошику.

Answer 1

Ответ:

пусть х количество яблок в первой корзинке после того, как переложили 6 яблок, у - во второй корзинке

х+у=60

2х=у

заменим у в первом уравнении

х+2х=60

3х=60

х=20 количество яблок в первой корзинке

у=40 во второй

х+6=26 в первой до перекладки

у-6=34 во второй до перекладки

Answer 2

Problem Analysis

We are given two baskets of apples. Initially, the total number of apples in both baskets is 60. After transferring 6 apples from the first basket to the second basket, the second basket has twice as many apples as the first basket. We need to determine the initial number of apples in each basket.

Solution

Let's assume the initial number of apples in the first basket is x, and the initial number of apples in the second basket is y.

According to the problem, the total number of apples in both baskets is 60. Therefore, we can write the equation:

x + y = 60 ---(Equation 1)

After transferring 6 apples from the first basket to the second basket, the second basket has twice as many apples as the first basket. Mathematically, we can represent this as:

y + 6 = 2(x - 6) ---(Equation 2)

Now, we can solve these two equations simultaneously to find the values of x and y.

Solving the Equations

Let's solve the equations using the substitution method.

From Equation 1, we can express x in terms of y:

x = 60 - y

Substituting this value of x into Equation 2, we get:

y + 6 = 2((60 - y) - 6)

Simplifying the equation:

y + 6 = 2(54 - y) y + 6 = 108 - 2y

Bringing all the y terms to one side:

y + 2y = 108 - 6 3y = 102

Dividing both sides by 3:

y = 34

Substituting the value of y back into Equation 1 to find x:

x + 34 = 60 x = 60 - 34 x = 26

Answer

Therefore, there were initially 26 apples in the first basket and 34 apples in the second basket.

Please let me know if anything is unclear or if you need further assistance!