Question

В зале кинотеатра количество рядов на 16 меньше, чем количество мест в ряду. Можно ли в этом зале разместить 6 классов учащихся для просмотра кинофильма, если в каждом из них 32 ученика? Задача с помощью квадратного уравнения

Answer 1

Пусть рядов x, тогда мест в ряду x+16, всего мест x*(x+16) = x^2+16x
и на них надо разместить  32*6 = 192 ученика. Составим и решим уравнение

x^2+16x = 192
x^2+16x -192 = 0
D= 16^2 + 4*192 = 256+ 768 = 1024  
корень(D) = 32
x1 = (-16+32)/2 = 8
x2 = (-16-32)/2 = -24 - не имеет смысла

ответ: можно, если будет 8 рядов по 24 места в каждом ряду
 

Answer 2

Problem Analysis

To solve this problem, we need to determine if it is possible to accommodate 6 classes of students, with 32 students in each class, in a cinema hall. The given information is that the number of rows in the cinema hall is 16 less than the number of seats in each row.

Let's assume the number of seats in each row is 'x'. According to the given information, the number of rows will be 'x - 16'. We need to find if it is possible to accommodate 6 classes of 32 students each in this cinema hall.

Solution

To solve this problem, we can set up an equation based on the given information and solve it using quadratic equation methods.

Let's set up the equation: Number of rows in the cinema hall = Number of seats in each row - 16

We can represent the number of rows in the cinema hall as 'x - 16'. Since there are 6 classes, each with 32 students, the total number of students is 6 * 32 = 192.

The total number of seats in the cinema hall is the product of the number of rows and the number of seats in each row, which is (x - 16) * x.

Now we can set up the equation: (x - 16) * x = 192

To solve this equation, we can rearrange it to a quadratic equation form: x^2 - 16x - 192 = 0

We can solve this quadratic equation to find the value of 'x' using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, 'a' is the coefficient of x^2, 'b' is the coefficient of x, and 'c' is the constant term.

Let's calculate the value of 'x' using the quadratic formula.

Calculation

Using the quadratic formula, we can calculate the value of 'x' as follows:

a = 1, b = -16, c = -192

x = (-(-16) ± √((-16)^2 - 4 * 1 * -192)) / (2 * 1) x = (16 ± √(256 + 768)) / 2 x = (16 ± √1024) / 2 x = (16 ± 32) / 2

Now we have two possible values for 'x': x1 = (16 + 32) / 2 = 48 / 2 = 24 x2 = (16 - 32) / 2 = -16 / 2 = -8

Since the number of seats cannot be negative, we can discard the value of x2.

Conclusion

The value of 'x' is 24, which represents the number of seats in each row of the cinema hall. Therefore, it is possible to accommodate 6 classes of 32 students each in this cinema hall.

Note: It is important to verify the accuracy of the solution by checking the calculations and assumptions made.