Question

A theater sells adult and child tickets to its plays. 2 adult tickets and 3 child tickets cost $30.75. 3 adult tickets and 2 child tickets cost $33.00. Let A represent the cost of 1 adult ticket, and C represent the cost of 1 child ticket. Which system of equations can be used to determine the cost of each type of ticket?

A) 2A + 3C = 30.75 and 3A + 2C = 33.00.
B) A + C = 30.75 and 3A + 2C = 33.00.
C) 2A + 3C = 30.75 and A + C = 33.00.
D) 3A + 2C = 30.75 and 2A + 3C = 33.00.

Answer 1

The correct system of equations to find the cost of adult and child theater tickets is 2A + 3C = 30.75 and 3A + 2C = 33.00, where A is the cost of an adult ticket and C is the cost of a child ticket.

Step-by-step explanation:

To determine the cost of each type of ticket at the theater using the information given, we can set up a system of equations. Let A represent the cost of 1 adult ticket, and C represent the cost of 1 child ticket. The first scenario gives us 2 adult tickets and 3 child tickets costing $30.75, which can be represented as 2A + 3C = 30.75. The second scenario with 3 adult tickets and 2 child tickets costing $33.00 gives us the equation 3A + 2C = 33.00. Therefore, the correct system of equations that can be used to determine the cost of adult and child tickets is Option A: 2A + 3C = 30.75 and 3A + 2C = 33.00.