Question

Devon purchased tickets to an air show for 9 adults and 2 children. The
total cost was $252. The cost of a childʹs ticket was $6 less than the cost of
an adultʹs ticket. Find the price of an adultʹs ticket and a childʹs ticket.

Answer 1

Let C be the cost of a child's ticket and A be the cost of an adult's ticket.
9 adults would spend 9A
2 children would spend 2C
If the total was 252, then 9A + 2C = 252
If the cost of a child's ticket is $6 less than the cost of an adult ticket, then C = A - 6
Substituting C = A - 6 into 9A + 2C = 252, we get
9A + 2(A - 6) = 252
9A + 2A - 12 = 252
11A - 12 = 252
11A = 264
A = 24

Substituting A = 22 into C = A - 6, we get
C = 24 - 6 = 18

Check
9 adult and 2 child's tickets would cost 9*24 + 2*18 = 216 + 36 = 252
The cost of a child's ticket, 18, is 6 less than the cost of an adult's ticket, 24.

So the cost of an adult's ticket is $24
and the cost of a child's ticket is $18.