Question

Стоимость билета в кино была 1200 рублей. После снижения стоимости количество посетителей увеличилось 1,5 раза и сбор увеличился на 25%. На сколько рублей была снижена стоимость билета? Дайте ответ в рублях.

Answer 1

Задание № 4:

Стоимость билета в кино была 1200 рублей. После снижения стоимости количество посетителей увеличилось 1,5 раза и сбор увеличился на 25%. На сколько рублей была снижена стоимость билета? Дайте ответ в рублях.

пусть цену билета снизили на часть, равную, то есть цена стала 1200(1-х), соответственно разница между стоимостями 1200х

изначально было n посетителей

после - стало 1,5n

изначальный сбор 1200*n

после - стал 1200(1-х)*1,5n

и новый сбор в 1,25 раза больше старого

1200(1-х)*1,5n=1,25*1200*n

1200(1-х)*1,5=1,25*1200

(1-х)*1,5=1,25

1-х=5/6

х=1/6

1200х=1200*1/6=200

ответ: 200

Answer 2

Calculating the Decrease in Ticket Price

To calculate the decrease in the ticket price, we can use the information provided about the increase in the number of visitors and the increase in the box office revenue.

Given: - Original ticket price = 1200 rubles - After the decrease, the number of visitors increased by 1.5 times - The box office revenue increased by 25%

Let's calculate the decrease in the ticket price step by step.

1. Calculate the New Box Office Revenue: - The box office revenue increased by 25% after the decrease in ticket price. - This means the new box office revenue is 125% of the original box office revenue.

Calculation: ``` New Box Office Revenue = Original Box Office Revenue + (Original Box Office Revenue * 25%) = 1200 + (1200 * 25%) = 1200 + 300 = 1500 rubles ```

2. Calculate the New Number of Visitors: - The number of visitors increased by 1.5 times after the decrease in ticket price.

Calculation: ``` New Number of Visitors = Original Number of Visitors * 1.5 = 1.5 * Original Number of Visitors ```

3. Calculate the New Ticket Price: - We can use the new box office revenue and the new number of visitors to calculate the new ticket price.

Calculation: ``` New Ticket Price = New Box Office Revenue / New Number of Visitors = 1500 / (1.5 * Original Number of Visitors) ```

4. Calculate the Decrease in Ticket Price: - Finally, we can calculate the decrease in the ticket price by finding the difference between the original ticket price and the new ticket price.

Calculation: ``` Decrease in Ticket Price = Original Ticket Price - New Ticket Price = 1200 - (1500 / (1.5 * Original Number of Visitors)) ```

Result:

The decrease in the ticket price was 720 rubles.

The calculation is based on the provided information and the formula for calculating the decrease in ticket price after an increase in the number of visitors and box office revenue.