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? СРОЧНО,ПОМОГИТЕ!!!И С ОБЪЯСНЕНИЯМИ В РАВНЕНИИ ЧТО С ЧЕМ СЛАДЫВАТЬ,НИЧЕГО НИГДЕ НЕ ПОНЯТНО

Answer 1

Problem Analysis

Let's break down the information given in the problem statement: - The total number of tickets purchased for a puppet theater is 70. - The number of tickets purchased for the parterre (main floor) is 1.5 times greater than the combined number of tickets purchased for the balcony and the dress circle. - The number of tickets purchased for the balcony is 0.4 times the number of tickets purchased for the dress circle.

We need to determine the number of tickets purchased for each section: parterre, balcony, and dress circle.

Solution

Let's assign variables to represent the number of tickets purchased for each section: - Parterre: P - Balcony: B - Dress Circle (Bel'etazh): D

We can set up the following equations based on the given information: 1. The total number of tickets purchased: P + B + D = 70 2. The number of tickets purchased for the parterre is 1.5 times greater than the combined number of tickets purchased for the balcony and the dress circle: P = 1.5 * (B + D) 3. The number of tickets purchased for the balcony is 0.4 times the number of tickets purchased for the dress circle: B = 0.4 * D

We can solve this system of equations to find the values of P, B, and D.

Solving the Equations

Let's substitute equation 3 into equation 2 to eliminate B: P = 1.5 * (0.4 * D + D) P = 1.5 * 1.4 * D P = 2.1 * D

Now, substitute the value of P from equation 2 into equation 1: 2.1 * D + B + D = 70 3.1 * D + B = 70

We can rearrange this equation to express B in terms of D: B = 70 - 3.1 * D

Now, substitute the value of B from the equation above into equation 3: 70 - 3.1 * D = 0.4 * D

Simplify the equation: 3.5 * D = 70

Solve for D: D = 70 / 3.5 D = 20

Now, substitute the value of D into equation 3 to find B: B = 0.4 * 20 B = 8

Finally, substitute the values of B and D into equation 1 to find P: P + 8 + 20 = 70 P = 70 - 8 - 20 P = 42

Answer

Therefore, the number of tickets purchased for each section is as follows: - Parterre: 42 tickets - Balcony: 8 tickets - Dress Circle (Bel'etazh): 20 tickets

I hope this helps! Let me know if you have any further questions.