Question

Сто орехов разложеныина пять кучек.В первой и второй вместе 52 ореха,во второй и третьей 43,в третьей и четвёртой 34, в четвертой и пятой 30.Сколько орехов в каждой кучке?

Answer 1

1)100÷5=20 (ор.)-в каждой кучке.
Ответ:20 орехов в каждой кучке.

Answer 2

1) x+y+z+u+v = 100;
2) x+y = 52;
3) y+z = 43;
4) z+u = 34;
5) u+v = 30;
сложим второе и пятое уравнения: x+y+u+v = 52+30 = 82;
вычтем полученное из первого уравнения, получим z = 100 - 82 =  = 18; зная количество предметов в третьей кучке (z), из третьего и четвертого уравнения получим:
y = 43 - z = 43 - 18 = 25;
u = 34 - z = 34 - 18 = 16;
Теперь из второго и пятого уравнения, получим:
x = 52 -y = 52 - 25 = 27;
v = 30 -u = 30 -16 = 14

Answer 3

Problem Analysis

We are given that there are 100 nuts divided into 5 piles. The number of nuts in each pair of adjacent piles is also given. We need to determine the number of nuts in each pile.

Solution

Let's assign variables to represent the number of nuts in each pile. We'll call them `x1`, `x2`, `x3`, `x4`, and `x5` for the first, second, third, fourth, and fifth piles, respectively.

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

1. `x1 + x2 = 52` (from the first and second piles) 2. `x2 + x3 = 43` (from the second and third piles) 3. `x3 + x4 = 34` (from the third and fourth piles) 4. `x4 + x5 = 30` (from the fourth and fifth piles)

We can solve this system of equations to find the values of `x1`, `x2`, `x3`, `x4`, and `x5`.

Solution Steps

1. Solve equation 1 for `x1`: `x1 = 52 - x2` 2. Substitute `x1` into equation 2: `52 - x2 + x2 + x3 = 43` Simplifying, we get: `x3 = 43 - 52 = -9` 3. Substitute `x1` into equation 3: `52 - x2 + x3 + x4 = 34` Simplifying, we get: `x4 = 34 - 52 + x2 - x3 = 18 + x2 - x3` 4. Substitute `x1` into equation 4: `52 - x2 + x4 + x5 = 30` Simplifying, we get: `x5 = 30 - 52 + x2 - x4 = -22 + x2 - x4` 5. Substitute the values of `x3`, `x4`, and `x5` into equation 2: `-9 + x2 + x3 = 43` Simplifying, we get: `x2 - 9 = 43` Solving for `x2`, we find: `x2 = 52` 6. Substitute the value of `x2` into equations 1, 3, and 4 to find `x1`, `x4`, and `x5`: - `x1 = 52 - x2 = 52 - 52 = 0` - `x4 = 18 + x2 - x3 = 18 + 52 - (-9) = 79` - `x5 = -22 + x2 - x4 = -22 + 52 - 79 = -49`

Answer

The number of nuts in each pile is as follows: - First pile: 0 nuts - Second pile: 52 nuts - Third pile: -9 nuts - Fourth pile: 79 nuts - Fifth pile: -49 nuts

Please note that having a negative number of nuts in a pile doesn't make sense in this context. It's possible that there was an error in the given information or in the calculations.