A group 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?

Can you send some answers. If not then I think $15 and $30.

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