Question

на 2 тарелках всего было по 10 яблок.когда с одной тарелки переложили на другую 2яблока,на обеих тарелках их стало поровну.сколько яблок было на каждой тарелки сначала?​

Answer 1

Problem Analysis

We are given that there were a total of 10 apples on two plates. When 2 apples were transferred from one plate to the other, the number of apples became equal on both plates. We need to determine how many apples were initially on each plate.

Solution

Let's assume that there were x apples on the first plate and y apples on the second plate initially.

According to the given information, the total number of apples on both plates is 10. Therefore, we can write the equation:

x + y = 10 (Equation 1)

After transferring 2 apples from one plate to the other, the number of apples becomes equal on both plates. This means that the number of apples on each plate is now equal to (x-2) and (y+2), respectively.

We can write another equation based on this information:

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

To solve this system of equations, we can substitute the value of (x-2) from Equation 2 into Equation 1:

x + y = 10 (Equation 1) x - 2 = y + 2 (Equation 2)

Substituting (x-2) into Equation 1, we get:

(y+2) + y = 10

Simplifying the equation, we have:

2y + 2 = 10

Subtracting 2 from both sides of the equation, we get:

2y = 8

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

y = 4

Now, we can substitute the value of y back into Equation 1 to find the value of x:

x + 4 = 10

Subtracting 4 from both sides of the equation, we get:

x = 6

Therefore, there were initially 6 apples on the first plate and 4 apples on the second plate.

Answer

There were initially 6 apples on the first plate and 4 apples on the second plate.