A group of 16 people bought tickets to a museum. They paid a total of $56. Each adult ticket costs $4 and each child ticket costs $2. Formulate and solve a system of equations to determine how many adult tickets and child tickets did they buy.
A: 4 adult tickets, 12 child tickets
B: 8 adult tickets, 8 child tickets
C: 10 adult tickets, 6 child tickets
D: 12 adult tickets, 4 child tickets
Let's denote the number of adult tickets by A and the number of child tickets by C.
From the given information, we can form the following system of equations:
1) A + C = 16 (equation representing the total number of tickets bought)
2) 4A + 2C = 56 (equation representing the total cost of the tickets)
To solve the system, we can use the method of substitution or elimination.
Let's use the method of substitution:
From equation 1, we can express A in terms of C as A = 16 - C.
Substituting this value of A into equation 2, we get:
4(16 - C) + 2C = 56
64 - 4C + 2C = 56
64 - 2C = 56
-2C = -8
C = 4
Substituting the value of C back into equation 1, we can find A:
A + 4 = 16
A = 12
Therefore, they bought 12 adult tickets and 4 child tickets.
The answer is option D: 12 adult tickets, 4 child tickets.