Question

Решите пожалуйста! Мама израсходовала половину денег и 1\3 остатка. У неё осталось 6000руб. Сколько денег было первоначально?

Answer 1

Problem Analysis

To solve this problem, we need to find the initial amount of money that the mother had before spending half of it and one-third of the remaining amount. We are given that the mother has 6000 rubles left after these expenses. Let's assume the initial amount of money is 'x' rubles.

Solution

1. The mother spent half of the money, which is x/2 rubles. 2. After this expense, she has (x - x/2) = x/2 rubles remaining. 3. She then spent one-third of the remaining amount, which is (x/2) * (1/3) = x/6 rubles. 4. After this expense, she has (x/2 - x/6) = (3x - x)/6 = 2x/6 = x/3 rubles remaining. 5. We are given that she has 6000 rubles left, so we can set up the equation: x/3 = 6000. 6. To solve for x, we can multiply both sides of the equation by 3: x = 6000 * 3 = 18000.

Answer

The initial amount of money that the mother had was 18000 rubles.

Verification

Let's verify the answer using the given information: 1. The mother spent half of the money: 18000/2 = 9000 rubles. 2. After this expense, she has 18000 - 9000 = 9000 rubles remaining. 3. She then spent one-third of the remaining amount: 9000 * (1/3) = 3000 rubles. 4. After this expense, she has 9000 - 3000 = 6000 rubles remaining, which matches the given information.

Therefore, the answer is verified to be correct.

Additional Information

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