Question

Помогите умоляю!!!В зрительном зале было 320 посадочных мест с равным количеством в каждом ряду .после того количество посадочных мест увеличили на 4 , и добавили еще один ряд то количество посадочных мест в зале стало 420 сколько рядов стало в зрительном зале?

Answer 1

Problem Analysis

We are given that there were initially 320 seats in the auditorium, with an equal number of seats in each row. After increasing the number of seats by 4 and adding one more row, the total number of seats became 420. We need to determine how many rows are now in the auditorium.

Solution

Let's assume that there were initially x rows in the auditorium. Since there were an equal number of seats in each row, we can calculate the number of seats in each row as 320 / x.

After increasing the number of seats by 4 and adding one more row, the total number of seats became 420. We can set up the following equation to represent this:

((320 / x) + 4) * (x + 1) = 420

To solve this equation, we can simplify it step by step:

1. Distribute the terms on the left side of the equation: (320 + 4x) * (x + 1) = 420

2. Expand the equation: 320x + 320 + 4x^2 + 4x = 420

3. Combine like terms: 4x^2 + 324x + 320 = 420

4. Move the constant term to the right side of the equation: 4x^2 + 324x - 100 = 0

Now, we can solve this quadratic equation to find the value of x (the number of rows).

Quadratic Equation Solution

We can solve the quadratic equation using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, the quadratic equation is 4x^2 + 324x - 100 = 0, so: - a = 4 - b = 324 - c = -100

Plugging these values into the quadratic formula, we get:

x = (-324 ± √(324^2 - 4 * 4 * -100)) / (2 * 4)

Simplifying further:

x = (-324 ± √(104976 + 1600)) / 8

x = (-324 ± √106576) / 8

x = (-324 ± 326) / 8

Now, we have two possible solutions for x:

1. x = (-324 + 326) / 8 = 2 / 8 = 0.25 2. x = (-324 - 326) / 8 = -650 / 8 = -81.25

Since the number of rows cannot be negative or a fraction, we can conclude that the number of rows in the auditorium is 0.25. However, this is not a valid answer, as the number of rows must be a whole number.

Conclusion

Based on the given information, it is not possible to determine the exact number of rows in the auditorium. The problem may have some inconsistencies or missing information. Please double-check the provided information or provide additional details to find a valid solution.