Question

Для учащихся было куплено 70 билетов в кукольный театр. В партер было куплено билетов в 1,5 раза больше, чем на балкон и бельэтаж вместе. Число билетов на балкон составило 0,4 от числа билетов на бельэтаж. Сколько билетов каждого вида было куплено?

Answer 1

на бельэтаж х

на балкон 0,4х

в партер (х+0,4х)*1,5=2,1х

всего 70

составим уравнение

х+0.4х+2,1х=70

3,5х=70

х=70:3,5

х=20 билетов на бельэтаж

20*0,4=8 билетов на балкон

2,1*20=42 билета в партер

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Answer 2

Problem Analysis

We are given the following information: - 70 tickets were purchased for a puppet theater. - The number of tickets for the parterre is 1.5 times greater than the combined number of tickets for the balcony and the bel étage. - The number of tickets for the balcony is 0.4 times the number of tickets for the bel étage.

We need to determine the number of tickets purchased for each type.

Solution

Let's assume the number of tickets for the bel étage is x.

According to the given information: - The number of tickets for the parterre is 1.5 times greater than the combined number of tickets for the balcony and the bel étage. Therefore, the number of tickets for the parterre is 1.5 * (x + 0.4x). - The number of tickets for the balcony is 0.4 times the number of tickets for the bel étage. Therefore, the number of tickets for the balcony is 0.4x. - The total number of tickets purchased is 70. Therefore, the equation becomes: x + 0.4x + 1.5 * (x + 0.4x) = 70.

Now, let's solve the equation to find the value of x.

Calculation

x + 0.4x + 1.5 * (x + 0.4x) = 70

Simplifying the equation: x + 0.4x + 1.5x + 0.6x = 70 3.5x = 70 x = 70 / 3.5 x = 20

Now that we have the value of x, we can calculate the number of tickets for each type: - Number of tickets for the bel étage: x = 20 - Number of tickets for the balcony: 0.4x = 0.4 * 20 = 8 - Number of tickets for the parterre: 1.5 * (x + 0.4x) = 1.5 * (20 + 0.4 * 20) = 1.5 * (20 + 8) = 1.5 * 28 = 42

Answer

Therefore, the number of tickets purchased for each type is as follows: - Bel étage: 20 tickets - Balcony: 8 tickets - Parterre: 42 tickets