SOLUTION: The manager of a theater wants to know whether the majority of its patrons are adults or children. One​ day, 5300 tickets were sold and the receipts totaled ​$40 co

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Question 1044289: The manager of a theater wants to know whether the majority of its patrons are adults or children. One​ day, 5300

tickets were sold and the receipts totaled ​$40 comma 981
.
The adult admission is ​$9.50
​,
and the​ children's admission is ​$6.50
.
How many adult patrons were​ there?
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
The manager of a theater wants to know whether the majority of its patrons are adults or children.
:
let a = the no. of adults
let c = no. of children
:
Write an equation for each statement
:
One​ day, 5300 tickets were sold
a + c = 5300
c = (5300-a); use this form for substitution
:
The adult admission is ​$9.50 and the​ children's admission is ​$6.50
the receipts totaled ​$40,981
9.50a + 6.50c = 40981
Replace c with (5300-a)
9.5a + 6.5(5300-a) = 40981
9.5a + 34450 - 6.5a = 40981
9.5a - 6.5a = 40981 - 34450
3a = 6531
a = 6531\3
a = 2177 adults
.
:
Confirm this solution; find the number of children
5300 - 2177 = 3123 children
Find the total receipts
9.5(2177) = 20681.50
6.5(3123) = 20299.50
---------------------
total rec'd: $40.981.00
.
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