Question

Вася живет на девятом этаже в доме, на каждом этаже которого имеется по шесть квартир. Его Товарищ Петя живет в квартире с тем же номером на седьмом этаже в доме, на каждом этаже которого имеется по семь квартир. Какой номер квартиры имеют мальчики?

Answer 1

49 я порахувала і в мене так вийшло

Answer 2

Answer in detail. Vasya lives on the ninth floor in a house, on each floor of which there are six apartments. His friend Petya lives in an apartment with the same number on the seventh floor in a house, on each floor of which there are seven apartments. What is the apartment number of the boys?

To answer this question, we need to find out the apartment number of Vasya and Petya based on the information given.

We can use the following formula to calculate the apartment number of any person living in a house:

$$\text{Apartment number} = (\text{Floor number} - 1) \times \text{Number of apartments per floor} + \text{Apartment position on the floor}$$

For example, if a person lives on the third floor in a house with five apartments per floor, and his apartment is the second one from the left, then his apartment number is:

$$(3 - 1) \times 5 + 2 = 12$$

Using this formula, we can find the apartment number of Vasya and Petya.

Since Vasya lives on the ninth floor in a house with six apartments per floor, and his apartment has the same number as Petya's, we can assume that his apartment position on the floor is also the same as Petya's. Let's call this position $x$. Then, Vasya's apartment number is:

$$(9 - 1) \times 6 + x = 48 + x$$

Similarly, since Petya lives on the seventh floor in a house with seven apartments per floor, and his apartment has the same number as Vasya's, we can use the same position $x$ for his apartment. Then, Petya's apartment number is:

$$(7 - 1) \times 7 + x = 42 + x$$

Since the apartment number of Vasya and Petya are the same, we can equate the two expressions and solve for $x$:

$$48 + x = 42 + x$$

Subtracting $x$ from both sides, we get:

$$48 = 42$$

This is a contradiction, since 48 is not equal to 42. Therefore, there is no such position $x$ that satisfies the given conditions. This means that there is no apartment number that is shared by both Vasya and Petya.

Hence, the answer to the question is: There is no such apartment number.