Question

A school fair ticket costs $8 per adult and $1 per child. On a certain day, the total number of adults (a) and children (c) who went to the fair was 30, and the total money collected was $100. Which of the following options represents the number of children and the number of adults who attended the fair that day, and the pair of equations that can be solved to find the numbers? 20 children and 10 adults Equation 1: a + c = 30 Equation 2: 8a + c = 100 10 children and 20 adults Equation 1: a + c = 30 Equation 2: 8a − c = 100 10 children and 20 adults Equation 1: a + c = 30 Equation 2: 8a + c = 100 20 children and 10 adults Equation 1: a + c = 30 Equation 2: 8a − c = 100

Answer 1

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".