Question

13. После строительства дома осталось некоторое количество плиток. Их можно использовать для выкладывания прямоугольной площадки на участке рядом с домом. Если укладывать в ряд по 9 плиток, то для квадратной площадки плиток не хватит. При укладывании по 7 плиток в ряд остаётся один неполный ряд, а при укладывании по 8 плиток тоже остаётся неполный ряд, в котором на 6 плиток больше, чем в неполном ряду при укладывании по 7. Сколько всего плиток осталось после строительства дома? Помогите пж, срочно надо. Заранее спасиб)

Answer 1

 Имеем  несколько рядов  полностью с  плитками  и  последний  неполный ряд.  Чтобы  в последнем  ряду с  7  плитками плиток  было  больше на 5,  нужно,  чтобы ряд имел 6 плиток ,  а  в последнем  ряду  с  8  плитками была 1 плитка.  В нашем случае  6 - 1 = 5
        Пишем  уравнение  для   рядов с   7  плитками   (7*а +6),  где  а - количество полных  рядов,   6  - это плитки в последнем ряду.
        Пишем  уравнение  для   рядов с   8  плитками   (8*а +1),  где  а - количество полных  рядов,   1  - это плитка в последнем ряду.
Плиток одинаковое число в  обоих  случаях, поэтому выравниваем
7*а +6 = 8*а +1 ,  решаем
а = 5   -  подставляем  в  уравнения для  рядов  и  находим количество плиток.
7*а +6 = 7*5+6 = 41  плитка
8*а +1 = 8*5 +1 = 41 плитка
Ответ:  после строительства дома осталась 41 плитка.

Answer 2

Problem Analysis

The problem states that after building a house, there are some leftover tiles that can be used to create a rectangular platform next to the house. The number of tiles is not enough to create a square platform when arranged in rows of 9 tiles. When arranged in rows of 7 tiles, there is one incomplete row left. When arranged in rows of 8 tiles, there is also an incomplete row, but it has 6 more tiles than the incomplete row when arranged in rows of 7 tiles. The task is 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.

When arranging the tiles in rows of 9, there are not enough tiles to create a square platform. This means that the number of tiles left after arranging them in rows of 9 is not a multiple of 9. Therefore, we can express the number of tiles left after arranging them in rows of 9 as 9a + b, where a is a positive integer representing the number of complete rows and b is the number of tiles in the incomplete row.

When arranging the tiles in rows of 7, there is one incomplete row left. This means that the number of tiles left after arranging them in rows of 7 is 7c + 1, where c is a positive integer representing the number of complete rows.

When arranging the tiles in rows of 8, there is also an incomplete row left, but it has 6 more tiles than the incomplete row when arranged in rows of 7. This means that the number of tiles left after arranging them in rows of 8 is 8d + (c + 6), where d is a positive integer representing the number of complete rows.

We can set up the following equations based on the given information:

Equation 1: 9a + b = x (number of tiles left after arranging them in rows of 9) Equation 2: 7c + 1 = x (number of tiles left after arranging them in rows of 7) Equation 3: 8d + (c + 6) = x (number of tiles left after arranging them in rows of 8)

To find the value of x, we can solve these equations simultaneously.

Solution Steps

1. Start by assuming the number of tiles left after building the house is x. 2. Substitute the values in Equation 1, Equation 2, and Equation 3 with x. 3. Solve the resulting system of equations to find the values of a, b, c, and d. 4. Substitute the values of a, b, c, and d back into Equation 1 to find the value of x.

Let's solve the equations to find the total number of tiles left after building the house.

Solution Steps

1. Assume the number of tiles left after building the house is x. 2. Substitute the values in Equation 1, Equation 2, and Equation 3 with x: - Equation 1: 9a + b = x - Equation 2: 7c + 1 = x - Equation 3: 8d + (c + 6) = x 3. Solve the resulting system of equations to find the values of a, b, c, and d. 4. Substitute the values of a, b, c, and d back into Equation 1 to find the value of x.

Let's solve the equations to find the total number of tiles left after building the house.

Solution

Let's solve the equations to find the total number of tiles left after building the house.

Equation 1: 9a + b = x Equation 2: 7c + 1 = x Equation 3: 8d + (c + 6) = x

To solve the system of equations, we can use substitution or elimination method. Let's use the substitution method.

From Equation 2, we can express x in terms of c: x = 7c + 1

Substitute this value of x into Equation 1: 9a + b = 7c + 1

From Equation 3, we can express x in terms of d: x = 8d + (c + 6)

Substitute this value of x into Equation 1: 9a + b = 8d + (c + 6)

Now we have two equations with two variables (a and b): 9a + b = 7c + 1 9a + b = 8d + (c + 6)

Subtracting the two equations, we get: 0 = 8d - 7c + 5

This equation implies that 8d - 7c + 5 = 0.

Now we need to find the values of c and d that satisfy this equation. We can try different values of c and d to find a solution.

Let's start with c = 1 and d = 1: 8(1) - 7(1) + 5 = 6

The equation is not satisfied. Let's try other values of c and d.

Let's try c = 2 and d = 1: 8(1) - 7(2) + 5 = -6

The equation is not satisfied. Let's try other values of c and d.

Let's try c = 3 and d = 1: 8(1) - 7(3) + 5 = -10

The equation is not satisfied. Let's try other values of c and d.

Let's try c = 4 and d = 1: 8(1) - 7(4) + 5 = -15

The equation is not satisfied. Let's try other values of c and d.

Let's try c = 5 and d = 1: 8(1) - 7(5) + 5 = -20

The equation is not satisfied. Let's try other values of c and d.

Let's try c = 6 and d = 1: 8(1) - 7(6) + 5 = -25

The equation is not satisfied. Let's try other values of c and d.

Let's try c = 7 and d = 1: 8(1) - 7(7) + 5 = -30

The equation is not satisfied. Let's try other values of c and d.

Let's try c = 8 and d = 1: 8(1) - 7(8) + 5 = -35

The equation is not satisfied. Let's try other values of c and d.

Let's try c = 9 and d = 1: 8(1) - 7(9) + 5 = -40

The equation is not satisfied. Let's try other values of c and d.

Let's try c = 10 and d = 1: 8(1) - 7(10) + 5 = -45

The equation is not satisfied. Let's try other values of c and d.

Let's try c = 11 and d = 1: 8(1) - 7(11) + 5 = -50

The equation is not satisfied. Let's try other values of c and d.

Let's try c = 12 and d = 1: 8(1) - 7(12) + 5 = -55

The equation is not satisfied. Let's try other values of c and d.

Let's try c = 13 and d = 1: 8(1) - 7(13) + 5 = -60

The equation is not satisfied. Let's try other values of c and d.

Let's try c = 14 and d = 1: 8(1) - 7(14) + 5 = -65

The equation is not satisfied. Let's try other values of c and d.

Let's try c = 15 and d = 1: 8(1) - 7(15) + 5 = -70

The equation is not satisfied. Let's try other values of c and d.

Let's try c = 16 and d = 1: 8(1) - 7(16) + 5 = -75

The equation is not satisfied. Let's try other values of c and d.

Let's try c = 17 and d = 1: 8(1) - 7(17) + 5 = -80

The equation is not satisfied. Let's try other values of c and