Question

билет на экскурсию в планетарий стоит 400рублей после снижения цены билета количества писетителей выросло на 20% а общий доход увеличился на 5%. На сколько рублей меньше стала цена билета?​

Answer 1

Ответ:

Цена билета стала меньше на 50 рублей.

Пошаговое объяснение:

Обозначим через x сумму, на которую снизилась стоимость билета, а через y – количество посетителей до снижения ценны билета. Тогда:

(400 – x) · 1,2y = 400y · 1,05

(400 – x) · 1,2 = 400 · 1,05

480 – 1,2x = 420

1,2x = 60

x = 50

Answer 2

To calculate the decrease in the ticket price, we need to determine the original price of the ticket and the new price after the decrease.

Let's assume the original price of the ticket to the planetarium was P rubles. After the decrease in price, the new ticket price became P - X rubles, where X is the decrease in price.

We are given the following information: - The original ticket price was 400 rubles. - The number of visitors increased by 20%. - The total revenue increased by 5%.

Calculating the new number of visitors:

To find the new number of visitors, we need to calculate 20% of the original number of visitors and add it to the original number of visitors.

Let's assume the original number of visitors was N. The new number of visitors is N + 0.2N = 1.2N.

Calculating the new total revenue:

To find the new total revenue, we need to calculate 5% of the original total revenue and add it to the original total revenue.

Let's assume the original total revenue was R. The new total revenue is R + 0.05R = 1.05R.

Calculating the new ticket price:

The new ticket price can be calculated by dividing the new total revenue by the new number of visitors.

The new ticket price is (P - X) = (1.05R) / (1.2N).

Now, let's solve for X, the decrease in the ticket price:

(P - X) = (1.05R) / (1.2N)

Simplifying the equation:

X = P - (1.05R) / (1.2N)

Substituting the given values: - P = 400 rubles - R = 400 rubles (since the total revenue increased by 5%) - N = 100 (assuming the original number of visitors was 100)

X = 400 - (1.05 * 400) / (1.2 * 100)

Calculating the value of X:

X = 400 - 420 / 120

X = 400 - 3.5

X ≈ 396.5

Therefore, the ticket price decreased by approximately 3.5 rubles.

Please note that the calculations provided above are based on the given information and assumptions.