Question

В погребе хранилось несколько головок сыра. Ночью пришли мышки и съели 8 головок сыра, причём все съели поровну. Следующей ночью пришли не все мышки,а только 15, и доели оставшийся сыр, но каждая мышка съела в четыре раза меньше сыра, чем накануне. Сколько головок сыра хранилось в погребе? Запишите решение и ответ.​

Answer 1

Ответ:

В погребе хранилось 11 головок сыра, а мышек было 55

Answer 2

Problem Analysis

In the cellar, there were several heads of cheese. The mice came at night and ate 8 heads of cheese, dividing them equally among themselves. The next night, only 15 mice came and finished the remaining cheese. However, each mouse ate four times less cheese than the previous night. We need to determine how many heads of cheese were originally stored in the cellar.

Solution

Let's assume that the original number of heads of cheese in the cellar is x.

On the first night, when all the mice were present, they ate 8 heads of cheese, dividing them equally among themselves. This means that each mouse ate 8/x heads of cheese.

On the second night, only 15 mice came, and each mouse ate four times less cheese than the previous night. Therefore, each mouse ate (8/x)/4 = 2/x heads of cheese.

The total amount of cheese eaten by the mice on the second night is given by: 15 * (2/x) = 30/x.

Since the total amount of cheese eaten on the second night is equal to the remaining cheese, we can set up the equation: 30/x = x - 8.

Let's solve this equation to find the value of x.

30/x = x - 8

Multiplying both sides by x:

30 = x^2 - 8x

Rearranging the equation:

x^2 - 8x - 30 = 0

We can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = -8, and c = -30.

x = (-(-8) ± √((-8)^2 - 4(1)(-30))) / (2(1))

Simplifying:

x = (8 ± √(64 + 120)) / 2

x = (8 ± √184) / 2

x = (8 ± 2√46) / 2

x = 4 ± √46

Since the number of heads of cheese cannot be negative, we take the positive root:

x = 4 + √46

Therefore, the original number of heads of cheese in the cellar was approximately 4 + √46.

Answer

The original number of heads of cheese in the cellar was approximately 4 + √46.