Question

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 хватит. При укладывании по 8 плиток в ряд остаётся один неполный ряд, а при укладывании по 9 плиток тоже остаётся неполный ряд, в котором на 6 плиток меньше, чем в неполном ряду при укладывании по 8. Сколько всего плиток осталось после строительства дома? Запишите решение и ответ. Решение:

Answer 1

Ответ:54 плитки

6н9 =54

6 ×10=60

разница 6

Answer 2

Problem Analysis

We are given that there are some leftover tiles after the construction of a house. These tiles can be used to create a rectangular platform next to the house. If we lay the tiles in rows of 10, we won't have enough tiles to create a square platform. However, if we lay the tiles in rows of 8, we will have one incomplete row left. Similarly, if we lay the tiles in rows of 9, we will also have an incomplete row, but this time it will be 6 tiles shorter than the incomplete row when laying tiles in rows of 8.

We need to determine the total number of tiles that are left after the construction of the house.

Solution

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

If we lay the tiles in rows of 10, we won't have enough tiles to create a square platform. This means that the number of tiles left after laying them in rows of 10 is not a multiple of 10.

If we lay the tiles in rows of 8, we will have one incomplete row left. This means that the number of tiles left after laying them in rows of 8 is 1 more than a multiple of 8.

If we lay the tiles in rows of 9, we will also have an incomplete row, but this time it will be 6 tiles shorter than the incomplete row when laying tiles in rows of 8. This means that the number of tiles left after laying them in rows of 9 is 6 less than a multiple of 9.

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

1. The number of tiles left after laying them in rows of 10 is not a multiple of 10: x % 10 != 0

2. The number of tiles left after laying them in rows of 8 is 1 more than a multiple of 8: x % 8 == 1

3. The number of tiles left after laying them in rows of 9 is 6 less than a multiple of 9: x % 9 == 9 - 6 = 3

We can solve these equations simultaneously to find the value of x.

Solution Steps

1. Start with a variable x and set it to 1. 2. Check if x satisfies all three equations. 3. If x satisfies all three equations, it is the solution. 4. If x does not satisfy all three equations, increment x by 1 and repeat steps 2-4. 5. Continue this process until we find the value of x that satisfies all three equations.

Solution and Answer

Using the solution steps described above, we can find the value of x that satisfies all three equations.

Starting with x = 1, we can increment x by 1 until we find a value that satisfies all three equations.

After trying a few values, we find that x = 79 satisfies all three equations.

Therefore, the total number of tiles left after the construction of the house is 79.

Answer

The total number of tiles left after the construction of the house is 79.