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.
Let's assume the number of adult tickets is "a" and the number of child tickets is "c".
From the problem, we know that:
a + c = 16 --> Equation 1 (The total number of tickets is 16)
4a + 2c = 56 --> Equation 2 (The total cost is $56)
To solve this system of equations, we can use the substitution method.
From Equation 1, we can express a in terms of c:
a = 16 - c
Substituting this value of a into Equation 2, we get:
4(16 - c) + 2c = 56
64 - 4c + 2c = 56
-2c = 56 - 64
-2c = -8
c = -8 / -2
c = 4
Now we can substitute the value of c into Equation 1 to find a:
a + 4 = 16
a = 16 - 4
a = 12
So, they bought 12 adult tickets and 4 child tickets.