Question

A school sells child and adult tickets to a play. The school sells a total of 65 tickets and collects a total of $382.50. The price of each child ticket is $4.50, and the price of each adult ticket is $6.50. Which system of equations can be used to determine the number of child tickets, x, and the number of adult tickets, y, they sold?

A. 6.50x + 4.50y = 65 x + y = 382.50
B. 4.50x + 6.50y = 65 x + y = 382.50
C. 6.50x + 4.50y = 382.50 x + y = 65
D. 4.50x + 6.50y = 382.50 x + y = 65

Answer 1

The correct system of equations that can be used to determine the number of child and adult tickets sold is 4.50x + 6.50y = 382.50 and x + y = 65.

Step-by-step explanation:

The correct system of equations that can be used to determine the number of child tickets, x, and the number of adult tickets, y, sold is:

4.50x + 6.50y = 382.50

x + y = 65

This system can be obtained by setting up two equations based on the given information:

1. Equation 1: The total number of tickets sold is 65. Since child tickets are represented by x and adult tickets by y, the equation becomes x + y = 65.
2. Equation 2: The total amount collected from ticket sales is $382.50. Using the prices of child and adult tickets, the equation becomes 4.50x + 6.50y = 382.50.

Therefore, the correct answer is option D: 4.50x + 6.50y = 382.50, x + y = 65.