The equation we will use is as follows
Aa + Cc = T
A= number of adults taking class
C = number of children taking class
a = cost of adult to take class
c = cost of child to take class
T = total costs
For this questions, they give us two scenarios :
1. 3 children and 2 adults for a total of $120
2. 5 children and 1 adult for a total of $95
Thus, we get the following equations :
1. 3c + 2a = 120
2. 5c + 1a = 95
This is a system of equations. Lets solve it!
solve the second equation for a and plug it into the first equation :
5c + 1a = 95
5c + a = 95
a = -5c + 95
Plug this into the first equation :
3c + 2a = 120
3c + 2(-5c + 95) = 120
3c - 10c + 190 = 120
- 7c = -70
c = 10
Thus, the cost for a child is $10. Now, plug c = 10 into our equation for a and solve for a.
a = -5c + 95
a = -5 (10) + 95
a = -50 + 95
a = $45
Thus, the cost for an adult is $45.
The total cost for one child and one adult is
Aa + Cc = T
1 (45) + 1 (10) = T
45 + 10 = T
55 = T
