SOLUTION: A state theater sold ticket for $500. Senior citizens receive a discount 20% and paid only $400. On the initial showing, the theater sold 450 ticket and registered a total of $2075
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Question 896321: A state theater sold ticket for $500. Senior citizens receive a discount 20% and paid only $400. On the initial showing, the theater sold 450 ticket and registered a total of $207500. How many of each type of ticket were sold?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A state theater sold ticket for $500.
Senior citizens receive a discount 20% and paid only $400.
On the initial showing, the theater sold 450 ticket and registered a total of $207500.
How many of each type of ticket were sold?
:
Let a = no. of adult tickets ($500)
let s = no. of seniors ($400)
:
The total tickets sold equation
a + s = 450
:
The total $ equation
500a + 400s = 207500
simplify, divide thru by 100
5a + 4s = 2075
:
Multiply the 1st equation by 4, use elimination with the above equation
5a + 4s = 2075
4a + 4s = 1800
----------------subtraction eliminates s, find a
a = 275 ea $500 tickets sold
Find s
450 - 275 = 175 ea $400 tickets sold
:
:
Check this: find amt for each type of ticket
275(500) = 137500
175(400) = 70000
------------------
total amt: 207500
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