SOLUTION: The manager of the Coral Theater wants to know whether the majority of its patrons are adults or children. One day in July, 5200 tickets were sold and the receipts totaled $29,961.
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Question 256643: The manager of the Coral Theater wants to know whether the majority of its patrons are adults or children. One day in July, 5200 tickets were sold and the receipts totaled $29,961. The adult admission is $7.50, and the children's admission is $4.50. How many adult patrons were there? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! One day in July, 5200 tickets were sold and the receipts totaled $29,961.
The adult admission is $7.50, and the children's admission is $4.50.
How many adult patrons were there?
:
a = no. of adults
c = no. of children
:
Total tickets equation
a + c = 5200
c = (5200-a); use this form for substitution
:
The total$ equation
7.50a + 4.50c = 29961
:
Replace c with (5200-a) from the 1st equation
7.5a + 4.5(5200-a) = 29961
:
7.5a + 23400 - 4.5a = 29961
:
7.5a - 4.5a = 29961 - 23400
:
3a = 6561
a =
a = 2,187 adults bought tickets
:
:
Check solution
5000 - 2187 = 3013 children
7.5(2187) + 4.5(3013) =
16402.50 + 13558.50 = 29961, confirms our solution
