Question

Четверо купцов заметили, что если они сложатся без первого, то соберут 90 рублей, без второго – 85, без третьего – 80, без четвертого – 75 рублей. Сколько у кого денег?

Answer 1

Всего денег у купцов (90 + 85 + 80 + 75) : 3 = 110 рублей. Поэтому у первого 110 – 90 = 20, у второго 110 – 85 = 25, у третьего 110 – 80 = 30, а четвертого 110 – 75 = 35 рублей

Answer 2

Пусть первый купец имеет х рублей, второй - у рублей, третий - z рублей, четвертый - w рублей.

Из условия задачи, мы можем составить следующую систему уравнений:

x + у + z + w = 90 у + z + w = 85 x + z + w = 80 x + у + w = 75

Выразим x из первого уравнения:

x = 90 - у - z - w

Подставим это значение x во второе уравнение:

у + z + w = 85 90 - у - z - w + z + w = 85 90 - у = 85 у = 90 - 85 у = 5

Теперь мы можем подставить это значение у в третье уравнение:

x + z + w = 80 90 - 5 - z - w + z + w = 80 90 - 5 = 80 x = 90 - 5 - 80 x = 5

И, наконец, подставим значения x и у в четвертое уравнение:

x + у + w = 75 5 + 5 + w = 75 10 + w = 75 w = 75 - 10 w = 65

Таким образом, у первого купца 5 рублей, у второго - 5 рублей, у третьего - 65 рублей и у четвертого - 65 рублей.

Answer 3

Problem Analysis

Four merchants have noticed that if they pool their money together without the first merchant, they will have 90 rubles. Without the second merchant, they will have 85 rubles. Without the third merchant, they will have 80 rubles. And without the fourth merchant, they will have 75 rubles. We need to determine how much money each merchant has.

Solution

Let's assign variables to represent the amount of money each merchant has. Let's call the first merchant A, the second merchant B, the third merchant C, and the fourth merchant D.

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

1. A + B + C + D - A = 90 2. A + B + C + D - B = 85 3. A + B + C + D - C = 80 4. A + B + C + D - D = 75

Simplifying these equations, we get:

1. B + C + D = 90 2. A + C + D = 85 3. A + B + D = 80 4. A + B + C = 75

Now we have a system of equations that we can solve to find the values of A, B, C, and D.

Let's solve this system of equations:

Adding equations 1, 2, 3, and 4, we get:

2A + 2B + 2C + 2D = 330

Dividing both sides by 2, we get:

A + B + C + D = 165

Subtracting equation 1 from this equation, we get:

A = 165 - 90 = 75

Substituting this value of A into equation 4, we get:

75 + B + C = 75

Simplifying, we get:

B + C = 0

Since B + C = 0, this means B = -C.

Substituting this into equation 3, we get:

75 + (-C) + C = 80

Simplifying, we get:

75 = 80

This equation is not possible, which means there is no solution to the system of equations. The given information is contradictory.

Therefore, it is not possible to determine how much money each merchant has based on the given information.

Conclusion: Based on the given information, it is not possible to determine how much money each merchant has. The given information is contradictory and does not lead to a consistent solution.