Question

Решить системой уравнений. Для класса, в котором учатся 30 учеников, купили билеты в театр стоимостью по 100 и 150 рублей. Сколько было куплено отдельно тех и других билетов, если их общая стоимость составила 3500 рублей?

Answer 1

X + y = 30
100x + 150y = 3500

x=30-y
100(30-y) + 150y=3500
3000-100y+150y=3500
50y=500
y=10 - билетов по 150 рублей
х=30-10=20 - билетов по 100 рублей

Answer 2

Solution:

Let's assume that the number of tickets bought at a cost of 100 rubles is represented by x, and the number of tickets bought at a cost of 150 rubles is represented by y.

We are given the following information: - The total number of students in the class is 30. - The total cost of all the tickets bought is 3500 rubles.

We can set up a system of equations to represent this information:

Equation 1: x + y = 30 (since the total number of tickets bought should equal the total number of students in the class)

Equation 2: 100x + 150y = 3500 (since the total cost of all the tickets bought is 3500 rubles)

To solve this system of equations, we can use the method of substitution or elimination.

Let's solve it using the method of substitution:

From Equation 1, we can express x in terms of y:

x = 30 - y

Substituting this value of x into Equation 2:

100(30 - y) + 150y = 3500

Simplifying the equation:

3000 - 100y + 150y = 3500

Combining like terms:

50y = 500

Dividing both sides by 50:

y = 10

Substituting this value of y back into Equation 1 to find x:

x + 10 = 30

x = 20

Therefore, the number of tickets bought at a cost of 100 rubles is 20, and the number of tickets bought at a cost of 150 rubles is 10.

Answer: The number of tickets bought at a cost of 100 rubles is 20, and the number of tickets bought at a cost of 150 rubles is 10.