Final answer:
A. To write a system of equations, let x represent the cost of an adult ticket and y represent the cost of a student ticket, e can set up the following system of equations:
2x + 3y = 27.50
x + 2y = 16.25
B. The cost of each adult ticket is $7.50 and the cost of each student ticket is $5.00.
C. Marsha's total cost for the additional tickets is $65.00.
Step-by-step explanation:
A. To write a system of equations to represent the situation, we can let x represent the cost of an adult ticket and y represent the cost of a student ticket. Based on the information given, we can set up the following system of equations:
2x + 3y = 27.50
x + 2y = 16.25
B. To determine the cost of each adult ticket and each student ticket, we can solve this system of equations using the method of substitution or elimination.
Solving the system of equations, we find that the cost of an adult ticket is $7.50 and the cost of a student ticket is $5.00.
C. To find Marsha's total cost for the additional tickets, we can multiply the number of adult tickets by the cost of an adult ticket and the number of student tickets by the cost of a student ticket, and then add the two amounts together. Marsha bought 4 adult tickets and 7 student tickets, so her total cost is
(4 * 7.50) + (7 * 5.00) = $30.00 + $35.00 = $65.00.