Let a be the number of adults which bought a ticket and c the number of children who bought a ticket. We can use the information given to assemble a system of equations.
Tickets cost 8 dollars for a, 1 dollar for c, and the total amount made is 100
8a + c = 100
The total of a and c is 30
a + c = 30
We can now subtract one equation from the other to use the elimination method to solve the system.
8a + c = 100
-(a + c = 30)
7a + 0 = 70
We can now solve for a.
7a = 70
a = 10
There were 10 adults who bought tickets. We can use this value as a known, plugging it into an equation to solve for the number of children.
a + c = 30
10 + c = 30
c = 20
So, the final answer is "20 children and 10 adults Equation 1: a + c = 30 Equation 2: 8a + c = 100".
