SOLUTION: Cindy is selling tickets to the circus. On her first day, she sold 4 adult tickets and 8 children's tickets for a total of $108. On the second day, she sold 5 adult tickets an

Algebra ->  Systems-of-equations -> SOLUTION: Cindy is selling tickets to the circus. On her first day, she sold 4 adult tickets and 8 children's tickets for a total of $108. On the second day, she sold 5 adult tickets an      Log On


   

Question 1183276: Cindy is selling tickets to the circus. On her first day, she sold 4 adult tickets and 8 children's tickets for a total of $108. On the second day, she sold 5 adult tickets and 6 children's tickets for a total of $105. What is the prices of an adult ticket and a Childs ticket?
Answer by greenestamps(13200) About Me  (Show Source):
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a = cost of adult ticket
c = cost of child ticket

4a+8c=108
5a+6c=105

Divide the first equation by the common factor of 4

a+2c=27

multiply by 5 to make the number of adult tickets the same as in the other equation

5a+10c=135

Compare the two equations

5a+10c=135
5a+6c=105
4c=30
c=7.50

The cost of each child ticket is $7.50

Substitute in either original equation to solve for the cost of an adult ticket

4a+8(7.50)=108
4a+60=108
4a=48
a=12

The cost of each adult ticket is $12

ANSWERS: adult ticket $12; child ticket $7.50