Question

В белом зале кинотеатра 874 мест, а в синем — 882. В белом зале на 2 ряда больше, чем в синем, но в каждом ряду на 4 места меньше, чем в каждом ряду синего зала. Сколько рядов в каждом зале кинотеатра? Ответ: В белом зале кинотеатра ? ряд(ов), в синем зале кинотеатра ? ряд(ов).

Answer 1

Пусть х число мест в ряду в белом зале тогда х+4 число мест в ряду в синем зале. Пусть у число рядов в белом зале тогда у-2 число рядов в синем зале.

Число мест в белом зале х*у=874 а в синем (х+4)(у-2)=882
-8+4у-2х=8
Получили систему уравнений
2у-х=8 выразил х и подставим во второе уравнение
ху=874

у*(2у+8)=874
У( у+4)=437 у^2+4у-437=0. у=42.
Ответ в белом зале 42 ряда в синем зале 40 рядов.

Answer 2

Problem Analysis

We are given information about the seating capacity of two different halls in a cinema. The white hall has 874 seats, while the blue hall has 882 seats. Additionally, we are told that the white hall has 2 more rows than the blue hall, but each row in the white hall has 4 fewer seats than each row in the blue hall. We need to determine the number of rows in each hall.

Solution

Let's assume that the number of rows in the blue hall is x. Therefore, the number of rows in the white hall would be x + 2.

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

1. The total number of seats in the white hall is 874: - Number of rows in the white hall * Number of seats per row in the white hall = 874 - (x + 2) * (Number of seats per row in the white hall) = 874

2. The total number of seats in the blue hall is 882: - Number of rows in the blue hall * Number of seats per row in the blue hall = 882 - x * (Number of seats per row in the blue hall) = 882

We can solve these equations simultaneously to find the values of x and Number of seats per row in the blue hall.

Let's solve the equations:

From equation 1: (x + 2) * (Number of seats per row in the white hall) = 874

From equation 2: x * (Number of seats per row in the blue hall) = 882

Since we have two unknowns, we need another equation to solve the system. However, we don't have any additional information to determine the number of seats per row in either hall. Therefore, we cannot find the exact values for the number of rows in each hall.

However, we can still provide a general solution. Let's assume the number of seats per row in the blue hall is y. Therefore, the number of seats per row in the white hall would be y - 4.

We can rewrite the equations as follows:

1. (x + 2) * (y - 4) = 874 2. x * y = 882

Unfortunately, without additional information, we cannot determine the exact number of rows in each hall. However, we can provide the general solution as shown above.

Please note that the above solution assumes that the number of seats per row in the blue hall is y. If you have any additional information or constraints, please let me know, and I'll be happy to assist you further.