Agroup of 3 children and 2 adults pay a total of $120 to take a karate class. a group of 5
children and 1 adult take the same karate class for $95. what is the total cost for 1 child
and 1 adult to take the karate class?

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

4, -4 is the other point it would pass through