Question

Во всех подъездах дома одинаковое число этажей,и на всех этажах одинаковое число квартир.При этом число этажей в доме больше числа квартир на этаже,число квартир на этаже больше числа подъездов,а число подъездов больше одного.Сколько этажей в доме,если всего в нем 455 квартир?

Answer 1

5-подъездов,7-квартир,13-этажей
455=5*7*13

Answer 2

Calculation of the Number of Floors in the Building

To determine the number of floors in the building, we can use the given information that there are a total of 455 apartments in the building, with an equal number of apartments on each floor and an equal number of floors in each entrance.

Let's assume that there are x floors in the building.

Since the number of apartments on each floor is greater than the number of entrances, and the number of entrances is greater than one, we can set up the following equation:

x * (x + 1) = 455

Simplifying the equation, we have:

x^2 + x - 455 = 0

We can solve this quadratic equation to find the value of x.

Using the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = 1, and c = -455.

Plugging in the values, we get:

x = (-1 ± √(1^2 - 4(1)(-455))) / (2(1))

Simplifying further:

x = (-1 ± √(1 + 1820)) / 2

x = (-1 ± √1821) / 2

Calculating the square root of 1821, we get:

x ≈ (-1 ± 42.7) / 2

Since the number of floors cannot be negative, we can ignore the negative solution.

Therefore, the number of floors in the building is approximately:

x ≈ (42.7 - 1) / 2 ≈ 41.7 / 2 ≈ 20.85

Since the number of floors must be a whole number, we can conclude that the building has 20 floors.

Please note that this calculation assumes that there are no additional factors or constraints mentioned in the question that could affect the number of floors in the building.