Question

В трёх ящиках лежали яблоки. В первом ящике на 5 кг меньше, чем в двух других вместе. А во втором – на 9 кг меньше, чем в двух других вместе. Сколько килограммов яблок в третьем ящике?

Answer 1

пусть x- первый ящик

y-второй

z-третий,тогда

y+z-x=5

z+x-y=9

затем складываем эти два уравнения и получаем,что z=7

Answer 2

Problem Analysis

We are given three boxes of apples. The first box weighs 5 kg less than the combined weight of the other two boxes, and the second box weighs 9 kg less than the combined weight of the other two boxes. We need to determine the weight of the apples in the third box.

Solution

Let's assume the weights of the apples in the three boxes are represented by variables: x for the first box, y for the second box, and z for the third box.

According to the given information: 1. The weight of the apples in the first box is 5 kg less than the combined weight of the other two boxes. This can be represented as: x = (y + z) - 5. 2. The weight of the apples in the second box is 9 kg less than the combined weight of the other two boxes. This can be represented as: y = (x + z) - 9.

We need to find the weight of the apples in the third box, which is represented by z.

To solve this system of equations, we can substitute the value of x from the first equation into the second equation and solve for y. Then, we can substitute the values of x and y into the first equation to solve for z.

Let's solve the equations step by step:

1. Substitute the value of x from the first equation into the second equation: (y + z) - 5 = (x + z) - 9

2. Simplify the equation: y + z - 5 = x + z - 9

3. Rearrange the equation: y - x = -4

4. Substitute the value of y - x into the first equation: x = (y + z) - 5

5. Substitute the value of y - x into the first equation: x = (y + z) - 5

6. Simplify the equation: x = y + z - 5

7. Substitute the value of y - x into the first equation: y + z - 5 = y + z - 5

8. Simplify the equation: 0 = 0

Since the equation simplifies to 0 = 0, it means that the system of equations is dependent, and there are infinitely many solutions. This means that we cannot determine the weight of the apples in the third box based on the given information alone.

Therefore, we cannot determine the weight of the apples in the third box based on the given information.

Please let me know if I can help you with anything else.