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

Calculation of the Ticket Price Reduction

To find out the amount by which the ticket price was reduced, we need to use the given information. Let's break down the problem step by step:

1. The original ticket price was 1200 rubles. 2. After the price reduction, the number of visitors increased by 1.5 times. 3. The collection (revenue) increased by 25%.

To solve this problem, we need to find the amount by which the ticket price was reduced.

Let's assume the reduced ticket price is x rubles.

According to the given information: 1. The number of visitors increased by 1.5 times, which means the new number of visitors is 1.5 times the original number of visitors. 2. The collection (revenue) increased by 25%, which means the new collection is 125% of the original collection.

To find the new collection, we can multiply the new number of visitors by the reduced ticket price: New Collection = (1.5 * Original Number of Visitors) * x

We can also express the new collection as 125% of the original collection: New Collection = 1.25 * Original Collection

Since the original collection is equal to the original number of visitors multiplied by the original ticket price, we can write: Original Collection = Original Number of Visitors * 1200 rubles

Now we can equate the two expressions for the new collection: (1.5 * Original Number of Visitors) * x = 1.25 * (Original Number of Visitors * 1200 rubles)

Simplifying the equation: 1.5x = 1.25 * 1200 rubles 1.5x = 1500 rubles x = 1500 rubles / 1.5 x = 1000 rubles

Therefore, the ticket price was reduced by 200 rubles.

Answer: The ticket price was reduced by 200 rubles.