Question

Две семьи отправились на детский утренник. Первая семья купила два детских билета и один взрослый и всего заплатила 415 рублей. Вторая семья купила три детских билета и два взрослых и всего заплатила 715 рублей. Сколько стоит один детский билет и сколько стоит один взрослый билет?

Answer 1

Ответ:

Цена детского билета - 115 рублей, цена взрослого - 185 рублей

Объяснение:

x - цена детского билета,

y - цена взрослого.

1) 2x + y = 415

y = 415 - 2x

2) 3x + 2y = 715

3x + 2( 415 - 2x) = 715

3x - 4x + 830 = 715

830 - x = 715

x = 830 - 715

x = 115 (руб)

3) y = 415 - 115 *2

y = 185 (руб)

Answer 2

Problem Analysis

We are given information about two families who went to a children's morning performance. The first family bought two children's tickets and one adult ticket for a total of 415 rubles. The second family bought three children's tickets and two adult tickets for a total of 715 rubles. We need to determine the cost of one children's ticket and one adult ticket.

Solution

Let's assume the cost of one children's ticket is x rubles and the cost of one adult ticket is y rubles.

From the given information, we can set up the following equations:

Equation 1: 2x + y = 415 (for the first family) Equation 2: 3x + 2y = 715 (for the second family)

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

Multiplying Equation 1 by 2, we get: 4x + 2y = 830

Subtracting Equation 2 from this new equation, we get: (4x + 2y) - (3x + 2y) = 830 - 715 x = 115

Now, we can substitute the value of x into Equation 1 to find y: 2(115) + y = 415 230 + y = 415 y = 415 - 230 y = 185

Therefore, the cost of one children's ticket is 115 rubles and the cost of one adult ticket is 185 rubles.

Answer

The cost of one children's ticket is 115 rubles and the cost of one adult ticket is 185 rubles.