Set up a system of equations for the following scenario. Then solve for the system. Three students buy different combinations of tickets for a baseball game. The first student buys 2 senior, 1 adult, and 2 student tickets for $51. The second student buys 1 adult and 5 student tickets for $55. The third student buys 2 senior, 2 adult, and 7 student tickets for $75. Set up a system of equations to find the price of each ticket.

Let

x = cost of a ticket for a senior

y = cost of a ticket for an adult

z = cost of a ticket for a student.

The first student buys 2 senior, 1 adult, and 2 student tickets for $51.

Therefore

2x + y + 2z = 51 (1)

Th second student buys 1 adult and 5 student tickets for $5.

Therefore

y + 5z = 55 (2)

The third student buys 2 senior, 2 adult, and 7 student tickets for $75.

Therefore

2x + 2y + 7z = 75 (3)

Answer:

The system of equation for determining x, y, and z is

2x + y + 2z = 51

y + 5z = 55

2x + 2y + 7z = 75

Warnng: The system of equations does not have a solution.