Question

После строительства дома осталось некоторое количество плиток. Их можно использовать для выкладки прямоугольной площадки на участке рядом с домом . Если укладывать в ряд по 10 плиток,то для квадратной площадки плиток не хватит. При вкладывании по8 плиток в ряд останется один неполный ряд,а при вкладывании по 9 - тоже останется неполный ряд, в котором на 6 плиток меньше, чем в неполном ряду при вкладывании по 8. Сколько всего плиток осталось после строительства дома? ПОЖАЛУЙСТА напишите решение по действиям не СЛОВЕСТНО

Answer 1

1) 6<остаток<8 (8+6)/2=7 плиток в остатке при выкладывании в ряд по 8.
2) 7-6=1 плитка в остатке при выкладывании по 9
3) 7-1=6 рядов по 8 и по 9 плиток.
4) 6*8+7=55 плиток было в остатке.
Проверка 6*9+1=55

Answer 2

Problem Analysis

We have a certain number of tiles left after building a house, and we want to use them to create a rectangular platform next to the house. If we lay the tiles in rows of 10, we won't have enough tiles for a square platform. If we lay them in rows of 8, we will have one incomplete row. If we lay them in rows of 9, we will also have an incomplete row, but with 6 fewer tiles than the incomplete row when laying them in rows of 8. We need to determine the total number of tiles left after building the house.

Solution

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

If we lay the tiles in rows of 10, the number of complete rows we can make is x / 10.

If we lay the tiles in rows of 8, the number of complete rows we can make is (x - 1) / 8 (since we have one incomplete row).

If we lay the tiles in rows of 9, the number of complete rows we can make is (x - 1) / 9 (since we have one incomplete row).

According to the problem statement, the number of tiles in the incomplete row when laying them in rows of 9 is 6 fewer than the number of tiles in the incomplete row when laying them in rows of 8. Therefore, we can write the equation:

(x - 1) / 9 = (x - 1) / 8 - 6

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

Solving the Equation

Expanding the equation, we get:

(x - 1) / 9 = (x - 1) / 8 - 6

Multiplying both sides of the equation by 9 and 8 to eliminate the denominators, we get:

8(x - 1) = 9(x - 1) - 6 * 9

Expanding and simplifying, we get:

8x - 8 = 9x - 9 - 54

Combining like terms, we get:

8x - 8 = 9x - 63

Subtracting 8x from both sides, we get:

-8 = x - 63

Adding 63 to both sides, we get:

55 = x

Therefore, the total number of tiles left after building the house is 55.

Answer

After building the house, there are 55 tiles left.