Question

Из кассы выдано 3/11 всех денег,потом 1/4 остатка,далее 2/7 нов остатка и 7/9 третьего остатка.После этого осталось 660 руб.Сколько денег было в начале?

Answer 1

Было-хруб
1раз выдано 3/11*хр
2-(х-3/11х)*1/4=8/11*х*1/4=2/11*хр
3-(8/11х-2/11х)*2/7=6/11*х*2/7=12/77*х*хр
4-(6/11-12/77х)*7/9=30/77*х*7/9=10/33*хр
Осталось 30/77х-10/33х=20/231*х=660р
х=660:20/231=660*231/20=33*231=7623р

Answer 2

Х денег в кассе
3х/11 выдано
(Х-3х/11=8х/11) остаток
8х/11*1/4=2х/11 выдано второй раз
(8х/11-2х/11=6х/11) остаток
6х/11*2/7=12/77 выдано третий раз
(6х/11-12/77=30х/77) остаток
(30х/77*7/9=10х/33) выдано четвертый раз
(30х/77-10х/33=20х/231) остаток
20х/231=660
Х=7623

Answer 3

Calculation of the Initial Amount of Money

To calculate the initial amount of money, we need to follow the given steps:

1. The total amount of money withdrawn from the cash register is 3/11 of the initial amount. 2. Then, 1/4 of the remaining balance is withdrawn. 3. Next, 2/7 of the new remaining balance is withdrawn. 4. Finally, 7/9 of the third remaining balance is withdrawn, leaving 660 rubles.

Let's calculate the initial amount of money step by step:

Step 1: The total amount of money withdrawn from the cash register is 3/11 of the initial amount.

Let's assume the initial amount of money is x rubles. Therefore, the amount withdrawn in the first step is (3/11)x rubles.

Step 2: 1/4 of the remaining balance is withdrawn.

After the first step, the remaining balance is (x - (3/11)x) rubles. Therefore, the amount withdrawn in the second step is (1/4)(x - (3/11)x) rubles.

Step 3: 2/7 of the new remaining balance is withdrawn.

After the second step, the new remaining balance is (x - (3/11)x) - (1/4)(x - (3/11)x) rubles. Therefore, the amount withdrawn in the third step is (2/7)[(x - (3/11)x) - (1/4)(x - (3/11)x)] rubles.

Step 4: 7/9 of the third remaining balance is withdrawn, leaving 660 rubles.

After the third step, the third remaining balance is [(x - (3/11)x) - (1/4)(x - (3/11)x)] - (2/7)[(x - (3/11)x) - (1/4)(x - (3/11)x)] rubles. According to the given information, this amount is equal to 660 rubles.

Now, we can solve the equation to find the initial amount of money, x.

Solution:

Let's solve the equation:

[(x - (3/11)x) - (1/4)(x - (3/11)x)] - (2/7)[(x - (3/11)x) - (1/4)(x - (3/11)x)] = 660

To simplify the equation, we can combine like terms:

[(8/11)x - (1/4)(8/11)x] - (2/7)[(8/11)x - (1/4)(8/11)x] = 660

Now, let's solve for x:

[(8/11)x - (2/11)x] - (2/7)[(8/11)x - (2/11)x] = 660

[(6/11)x] - (2/7)[(6/11)x] = 660

[(6/11)x] - (12/77)x = 660

To combine the terms with x, we need a common denominator:

[(42/77)x - (12/77)x] = 660

[(30/77)x] = 660

Now, we can solve for x:

x = (660 * 77) / 30

x = 1694

Therefore, the initial amount of money was 1694 rubles.

Please note that the calculation is based on the given information and assumptions made during the calculation process.