Question

На трѐх банковских картах имелось в сумме 3000 рублей. На третьей карте было в 2 раза больше, чем на остальных картах вместе, а на первой карте – третья часть той суммы, что была на остальных картах вместе. Какая сумма была на каждой банковской карте?

Answer 1

Problem Analysis

We are given three bank cards with a total of 3000 rubles. The amount on the third card is twice the amount on the other two cards combined, and the amount on the first card is one-third of the total amount on the other two cards. We need to find the amount on each bank card.

Solution

Let's assume the amounts on the first, second, and third cards are x, y, and z rubles, respectively.

From the given information, we can form the following equations: 1. x + y + z = 3000 (equation 1) 2. z = 2(x + y) (equation 2) 3. x = (1/3)(x + y) (equation 3)

To solve these equations, we can substitute equation 3 into equation 1 and solve for x.

Calculation

Let's substitute equation 3 into equation 1: (1/3)(x + y) + y + z = 3000 (x + y) + 3y + 3z = 9000 4x + 4y + 4z = 9000

Now, let's substitute equation 2 into the above equation: 4x + 4y + 8(x + y) = 9000 4x + 4y + 8x + 8y = 9000 12x + 12y = 9000

Dividing both sides of the equation by 12: x + y = 750

Now, let's substitute this value back into equation 3 to find the value of x: x = (1/3)(x + y) x = (1/3)(750) x = 250

Substituting the value of x back into equation 1, we can find the value of y: 250 + y + z = 3000 y + z = 2750

Substituting the value of z from equation 2 into the above equation: y + 2(x + y) = 2750 y + 2y + 2x = 2750 3y + 2x = 2750

Substituting the values of x and y from the previous calculations: 3y + 2(250) = 2750 3y + 500 = 2750 3y = 2250 y = 750

Finally, substituting the values of x and y into equation 1, we can find the value of z: 250 + 750 + z = 3000 z = 2000

Answer

The amounts on each bank card are as follows: - The first card has 250 rubles. - The second card has 750 rubles. - The third card has 2000 rubles.

Note: The solution provided above is based on the given information and mathematical calculations.