Devon purchased tickets to an air show for 9 adults and 2 children. the total cost was $252. the cost of a child's ticket was $6 less than the cost of an adult's ticket. find the price of an adult's ticket and a child's ticket.

A=cost of 1 adult ticket
c=cost of 1 child ticket

so
9a+2c=252
and
c=a-6
sub a-6 for c

9a+2(a-6)=252
9a+2a-12=252
11a-12=252
add 12 both sides
11a=264
divide both sides by 11
a=24

sub back
c=a-6
c=24-6
c=18

adult ticket costs $24 and child ticket costs $18