Home > Math > Detail

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.


By using a system of equations, it has been determined that the cost of both the orchestra ticket and balcony ticket is $10 each, and the quantities are equal. A system of equations is a set of equations where two or more variables are related, and their values are found by solving the equations together. In this problem, variable a denotes the cost of an orchestra ticket and variable b denotes the cost of a balcony ticket. Peter paid $50 for one orchestra and four balcony tickets, so a + 4b = 50, which can be rewritten as a = 50 - 4b. Justine paid $150 for three orchestra and twelve balcony tickets, so 3a + 12b = 150. Since a is equal in both equations, we assume that the costs are equal, meaning a + 4b = 50. Solving for a in this equation, we get a = 10. Hence, the cost of both orchestra and balcony tickets is $10 each, and their quantities are equal. For further information on systems of equations, visit brainly.com/question/24342899 #SPJ1.