Question

A group of 3 children and 2 adults pay a total of $121 to take a karate class. A group of 5 children and

1 adult take the same karate class for $85. What is cost per adult and per child? Write and solve a
system of equations.

Answer 1

The cost for a child is $7 and the cost for an adult is $50

Explanation:

Let 'x' represent children

Let 'y' represent adults

The equations used to come to this answer are:

`3x + 2y = 121 \\ 5x + 1y = 85`

`3x + 2y = 121 \\ 5x( - 2) + 1y( - 2) = 85( - 2) \\ \\ 3x + 2y = 121 \\ - 10x - 2y = - 170 \\ - 7x = - 49`

Therefore; x = 7

`5x + 1y = 85 \\ 5(7) + y = 85 \\ 35 + y = 85 \\ y = 85 - 35 \\ y = 50`