Question

Решить задачу составив систему . Для класса купили 30 билетов в театр по 10 рублей и15 рублей . За все билеты заплатили 390 рублей. Сколько купили билетов за 10 рублей и сколько за 15 рублей

Answer 1

Пусть билетов по 10 руб  - х штук, а билетов по 15 руб  - у штук.

Тогда из условия имеем систему:

х + у = 30                  у = 30 - х

10х + 15у = 390         10х + 15(30-х) = 390

 

у = 30-х             у = 18

5х = 60              х = 12

Ответ: 10-рублевых -  12 штук;  15-рублевых -  18 штук.

Answer 2

x - билеты по 10 рублей 

y -   билеты по 15 рублей   

 

x+y=30

10x+15y=390

 

x=30-y

10x+15y=390

 

10(30-y)+15y=390

300-10y+15y=390

5y=90

y=18

 

x=30-18

x=12

 

 

Answer 3

Problem Analysis

To solve this problem, we need to find the number of tickets purchased at 10 rubles and the number of tickets purchased at 15 rubles. We are given that a total of 30 tickets were purchased, and the total cost of all the tickets was 390 rubles.

Solution

Let's assume that x tickets were purchased at 10 rubles each, and y tickets were purchased at 15 rubles each. We can set up a system of equations to represent the given information:

Equation 1: x + y = 30 (since a total of 30 tickets were purchased) Equation 2: 10x + 15y = 390 (since the total cost of all the tickets was 390 rubles)

We can solve this system of equations to find the values of x and y.

Solving the System of Equations

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From Equation 1, we can express x in terms of y as x = 30 - y. We can substitute this value of x into Equation 2:

10(30 - y) + 15y = 390 300 - 10y + 15y = 390 5y = 90 y = 18

Now that we have the value of y, we can substitute it back into Equation 1 to find the value of x:

x + 18 = 30 x = 30 - 18 x = 12

Therefore, 12 tickets were purchased at 10 rubles each, and 18 tickets were purchased at 15 rubles each.

Answer

The number of tickets purchased at 10 rubles is 12, and the number of tickets purchased at 15 rubles is 18.