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 хватает. При укладывании по 8 плиток в ряд остаётся один не полный ряд, а при укладывании по 9 - 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? Решите плз ^_^, а то завтра у меня ВПР по математике (((

Answer 1

Решение и  ответ в приложении.
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Answer 2

Problem Analysis

To solve this problem, we need to determine the total number of tiles left after constructing the house. We are given that if the tiles are laid out in rows of 10, there will be a shortage for a square platform. Similarly, if the tiles are laid out in rows of 8 or 9, there will be an incomplete row with fewer tiles than the incomplete row when laid out in rows of 8. We need to find the total number of tiles left.

Solution

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

If the tiles are laid out in rows of 10, there will be a shortage for a square platform. This means that the number of tiles left is not a multiple of 10. Therefore, we can write the equation:

x ≠ 10k (where k is an integer)

If the tiles are laid out in rows of 8, there will be an incomplete row with fewer tiles than the incomplete row when laid out in rows of 8. This means that the number of tiles left is not a multiple of 8. Therefore, we can write the equation:

x ≠ 8m (where m is an integer)

If the tiles are laid out in rows of 9, there will be an incomplete row with fewer tiles than the incomplete row when laid out in rows of 8. This means that the number of tiles left is not a multiple of 9. Therefore, we can write the equation:

x ≠ 9n (where n is an integer)

From the given information, we can conclude that the number of tiles left is not a multiple of 10, 8, or 9.

To find the total number of tiles left, we need to find the smallest positive integer that satisfies all three conditions above.

Finding the Solution

To find the smallest positive integer that satisfies all three conditions, we can use the concept of the least common multiple (LCM). The LCM of 10, 8, and 9 will give us the smallest positive integer that is not a multiple of any of these numbers.

The LCM of 10, 8, and 9 is 360.

Therefore, the total number of tiles left after constructing the house is 360.

Answer

The total number of tiles left after constructing the house is 360.