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
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Let's assume the number of adult tickets is a and the number of child tickets is c.
From the given information, we know that:
a + c = 16 (equation 1)
4a + 2c = 56 (equation 2)
To solve the system of equations, we can either use substitution or elimination method.
Using the substitution method:
From equation 1, we have c = 16 - a
Substituting this value of c into equation 2, we get:
4a + 2(16 - a) = 56
Simplifying, we have:
4a + 32 - 2a = 56
Combining like terms:
2a + 32 = 56
Subtracting 32 from both sides:
2a = 24
Dividing both sides by 2:
a = 12
Substituting the value of a into equation 1, we get:
12 + c = 16
Subtracting 12 from both sides:
c = 4
Therefore, they bought 12 adult tickets and 4 child tickets.
The correct answer is D. 12 adult tickets, 4 child tickets.