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.

Answer 1

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.