A local movie theater charges $12 for an adult ticket and $10 for a child's ticket. A group of 8 people spent a total of $86 on tickets to a movie. How many adults and how many children were in the group? Write a system of linear equations based on the description. Use X to represent the number of adults and Y to represent the number of children.

Total price paid: 86=12*X +10*YTotal number of people: 8=X + YHence Y=8-X thus 86=12*X +10 (8-X) => 86-80=2X => X=3 => Y=5There were 3 adults and 5 children