Question 1098840
Cindy is selling tickets. she sold 8 adults tickets and 5 children's tickets for a total of $177.50 in sales.
 The second day she received $255.00 for 12 adult tickets and 6 children tickets.
 What is the price of a child's ticket?
 What is the price of an adult ticket? 
:
let a = price of an adult ticket
let c = price of a child's
:
Write an equation for each day
8a + 5c = 177.50
12a + 6c = 255.0
Use the above equation for substitution
12c + 6c = 255.0
6c = -12a + 255
Divide both sides by 6
c = -2a + 42.5
:
In the first equation, replace c with (-2a+42.5)
8a + 5(-2a+42.5) = 177.50
8a - 10a + 212.5 = 177.5
-2a = 177.5 - 212.5
-2a = -35
a = -35/-2
a = $17.50 is the cost of an adult ticket
Find the child's ticket cost
c = -2(17.5) + 42.5
c = -35 + 42.5
c = $7.50 is cost of a child's ticket
:
:
Confirm this in the original 2nd equation
12(17.5) + 6(7.5) = 255
210 + 45 = 255