Question

Нюша вырезала пятиугольник и шестиугольник.Всего у них 27 вершин.Сколько шестиугольников вырезала Нюша?

Answer 1

Если бы Нюша вырезала одни пятиугольники, то всего вершин было бы:

27 : 5 = 5 (ост. 2) - т.е. эти 2 вершины - "лишние", которые и принадлежат двум шестиугольникам.

5 - 2 = 3 фигуры - пятиугольники.

Проверим:

3 * 5 + 2 * 6 = 27 вершин - всего.

Ответ: Нюша вырезала два шестиугольника.

Answer 2

Наверное, Нюша вырезала несколько пятиугольников и несколько шестиугольников?..))

Предположим, что все фигуры, которые вырезала Нюша, - пятиугольники.

Тогда количество вершин должно быть кратно 5, то есть 25.

Оставшиеся 2 вершины, очевидно, принадлежат шестиугольникам..))

В двух шестиугольниках: 6 * 2 = 12 вершин.

Оставшиеся вершины: 27 - 12 = 15 принадлежат пятиугольникам и их, соответственно: 15 : 5 = 3 (шт.)

Всего 5 фигур: шестиугольников - 2, пятиугольников - 3.

---------------------------

Ответ: Нюша вырезала 2 шестиугольника.

Answer 3

Problem Analysis

In this problem, we are given that Nyusha cut out a pentagon and a hexagon, and the total number of vertices in both shapes is 27. We need to determine how many hexagons Nyusha cut out.

Solution

Let's assume that Nyusha cut out x hexagons. Since each hexagon has 6 vertices, the total number of vertices in the hexagons would be 6x.

Similarly, let's assume that Nyusha cut out y pentagons. Since each pentagon has 5 vertices, the total number of vertices in the pentagons would be 5y.

According to the problem, the total number of vertices in both shapes is 27. Therefore, we can write the equation:

6x + 5y = 27

To find the number of hexagons Nyusha cut out, we need to solve this equation.

Solving the Equation

To solve the equation, we can use a method called substitution. Let's solve for x in terms of y:

6x = 27 - 5y x = (27 - 5y) / 6

Now, we can substitute this value of x back into the equation:

6((27 - 5y) / 6) + 5y = 27

Simplifying the equation:

27 - 5y + 5y = 27 27 = 27

The equation simplifies to 27 = 27, which is true. This means that the equation is satisfied for any value of y.

Therefore, there can be any number of pentagons that Nyusha cut out, and the number of hexagons can be calculated using the equation:

x = (27 - 5y) / 6

So, the number of hexagons Nyusha cut out depends on the number of pentagons she cut out.

Conclusion

In conclusion, the number of hexagons that Nyusha cut out depends on the number of pentagons she cut out. The equation to calculate the number of hexagons is x = (27 - 5y) / 6, where x is the number of hexagons and y is the number of pentagons.