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A theater sells 2 types of fixed-price tickets - orchestra and balcony. Peter pays $50 for 1 orchestra and 4 balcony tickets. Justine pays $150 for 3 orchestra and 12 balcony tickets. А B The cost of 1 balcony ticket. The cost of 1 orchestra ticket. The quantity under A is greater than the quantity under B. The quantity under B is greater than the quantity under A. The quantities under A and B are equal. The information given is insufficient to make the comparison.

Respuesta :

Using a system of equations, it is found that:

  • The cost of an orchestra ticket is of $10.
  • The cost of a balcony ticket is of $10.
  • The quantities are equal.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

  • Variable a: Cost of an orchestra ticket.
  • Variable b: Cost of a balcony ticket.

Peter pays $50 for 1 orchestra and 4 balcony tickets, hence:

a + 4b = 50 -> a = 50 - 4b.

Justine pays $150 for 3 orchestra and 12 balcony tickets, hence:

3a + 12b = 150.

a + 4b = 50 -> a = 50 - 4b.

The equations are equal, hence we suppose that the costs are equal, that is:

a + 4b = 50 -> 5a = 50 -> a = 10.

Hence:

  • The cost of an orchestra ticket is of $10.
  • The cost of a balcony ticket is of $10.
  • The quantities are equal.

More can be learned about a system of equations at https://brainly.com/question/24342899

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