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

A + c = 30 ....a = 30 - c
8a + c = 100

8(30 - c) + c = 100
240 - 8c + c = 100
-8c + c = 100 - 240
-7c = - 140
c = -140/-7
c = 20 <== children

a + c = 30
a + 20 = 30
a = 30 - 20
a = 10 <== adults

Answer 2

The right equations are a+c=30 (total number of people) and 8a+c=100 (total amount of money). So answers B and D cannot be right.

a+c=30 can be rewritten as c=30-a and filled into the second one:

8a + 30-a = 100 => 7a = 70 => a=10

That leaves answer A as the right one.