Question 1109117: Lynn is selling tickets to the school play. On the first day of ticket sales she sold 5 adult tickets and 9 children tickets for a total of $98.75. On the second day she sold 10 adult tickets and 15 children tickets for a total of $182.50. What is the price for one adult ticket and one student ticket?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Lynn is selling tickets to the school play.
On the first day of ticket sales she sold 5 adult tickets and 9 children tickets for a total of $98.75. On the second day she sold 10 adult tickets and 15 children tickets for a total of $182.50.
What is the price for one adult ticket and one student ticket?
:
let a = the price of adult tickets
let c = the price of children's
:
Write an equation for each day
5a + 9c = 98.75
10a + 15c = 182.50
Use elimination, multiply the 1st equation by 2
10a + 18c = 197.50
10a + 15c = 182.50
----------------------subtraction eliminates a, find c
0 + 3c = 15
c = 15/3
c = $5 for each child
:
Find a
5a + 9(5) = 98.75
5a + 45 = 98.75
5a = 98.75 - 45
5a = 53.75
a = 53.75/5
a = $10.75 for each adult
:
:
Check this using the 2nd equation, replace a and c
10a + 15c = 182.50
10(10.75) + 15(5) =
107.50 + 75 = 182.50
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