Question 1098840: Please help me solve this equations
The circus is coming. 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?
Write two algebraic equations that model this circus ticket scenario.
Show how you solved the problem by using elimination method, the substitution method, or the graphical method
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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
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