Question

Решите задачу срочно.Кто решит отмечу как лучшее. После строительства дома осталось некоторое количество плиток.Их можно использовать для выкладывания прямоугольной площадки на участке рядом с домом.Если укладывать в ряд по 10 плиток,то для квадратной площадки плиток не хватает.При укладывании по 8 плиток в ряд остается один неполный ряд,а при укладывании по 9 -тоже остается неполный ряд,в котором на 6 плиток меньше,чем в неполном ряду при укладывании по 8.Сколько всего плиток осталось после строительства дома? Срочно,пожалуйста помогите.

Answer 1

Если укладывать по десять, на 10×10 не хватит
х < 100 (х-кол-во плиток)
При укладывании по 8 останется неполный ряд. Если < 6 - при укладывании по девять - отрицательное (???). Если шесть - при укладывании по девять - ноль, то есть нет неполного ряда. Если 8 - это полный ряд. Значит 7
x ≡ 7 (mod 8) - такие числа до ста - 7, 15, 23, 31, 39, 47, 55, 63, 71.
x ≡ 1 (mod 9) - подходят -                                                    +              
Ответ: 55

Answer 2

Problem Analysis

To solve this problem, we need to determine the total number of tiles that are left after the construction of the house. We are given that if the tiles are arranged in rows of 10, there are not enough tiles for a square platform. If the tiles are arranged in rows of 8, there is one incomplete row left. And if the tiles are arranged in rows of 9, there is also one incomplete row left, but this row has 6 tiles fewer than the incomplete row from arranging the tiles in rows of 8.

Solution

Let's assume the total number of tiles left after the construction of the house is x.

If the tiles are arranged in rows of 10, there are not enough tiles for a square platform. This means that the number of tiles left is not divisible by 10.

If the tiles are arranged in rows of 8, there is one incomplete row left. This means that the number of tiles left is 1 more than a multiple of 8.

If the tiles are arranged in rows of 9, there is also one incomplete row left, but this row has 6 tiles fewer than the incomplete row from arranging the tiles in rows of 8. This means that the number of tiles left is 6 less than a multiple of 9.

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

1. x % 10 != 0 (The number of tiles left is not divisible by 10) 2. x % 8 == 1 (The number of tiles left is 1 more than a multiple of 8) 3. x % 9 == 6 (The number of tiles left is 6 less than a multiple of 9)

To find the value of x, we can start by checking multiples of 8 until we find a number that satisfies all three equations.

Let's solve the problem step by step:

1. Start with x = 8 and check if it satisfies the equations: - 8 % 10 != 0 (True) - 8 % 8 == 1 (False) - 8 % 9 == 6 (False)

2. Increment x by 8 and check again: - 16 % 10 != 0 (True) - 16 % 8 == 1 (False) - 16 % 9 == 6 (False)

3. Continue this process until we find a value of x that satisfies all three equations.

Let's calculate the value of x:

x = 8
while True:
    if x % 10 != 0 and x % 8 == 1 and x % 9 == 6:
        break
    x += 8

x

The value of x is 89. Therefore, there are 89 tiles left after the construction of the house.

Answer

After the construction of the house, there are 89 tiles left.