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? (4 points)
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
a + c = 30
8a + c = 100
================== subtract
-7 a = -70
a = 10
then c = 20
The correct option is:
20 children and 10 adults
Equation 1: a + c = 30
Equation 2: 8a + c = 100
The correct option is:
20 children and 10 adults
Equation 1: a + c = 30
Equation 2: 8a + c = 100
To find the numbers of adults and children who attended the fair, we can set up a system of equations. Let's let a represent the number of adults and c represent the number of children.
Equation 1 represents the total number of people who attended the fair: a + c = 30.
Equation 2 represents the total amount of money collected: 8a + c = 100.
To solve this system of equations, we can use a variety of methods such as substitution or elimination.
For the given problem, let's solve the system of equations using elimination:
Start with the two equations:
a + c = 30
8a + c = 100
To eliminate the variable c, we can subtract Equation 1 from Equation 2:
(8a + c) - (a + c) = 100 - 30
7a = 70
Divide both sides of the equation by 7 to solve for a:
a = 10
Now that we have the value of a, we can substitute it back into Equation 1 to find the value of c:
10 + c = 30
c = 20
Therefore, the correct option is 20 children and 10 adults, and the pair of equations that can be solved to find the numbers are:
Equation 1: a + c = 30
Equation 2: 8a + c = 100
On a certain day, the total number of adults (a) and children (c) who went to the fair was 30 mean:
a + c = 30
A school fair ticket costs $8 per adult and $1 per child. The total money collected was $100 mean:
$8 ∙ a + $1 ∙ c = $100
8 a + c = 100
a + c = 30
8 a + c = 100
When you solve this system, solution is:
a = 10 , c = 20
10 adults and 20 children
Proof:
a + c = 10 + 20 = 30
$8 ∙ a + $1 ∙ c =
$8 ∙ 10 + $1 ∙ 20 =
$80 + $20 = $100