SOLUTION: The manager of the Coral Theater wants to know whether the majority of its patrons are adults or children. During a week in July, 5200 tickets were sold and the receipts totaled $2

Question 507902: The manager of the Coral Theater wants to know whether the majority of its patrons are adults or children. During a week in July, 5200 tickets were sold and the receipts totaled $20,335. The adult admission is $4.75 and the children's admission is $2.50. How many adult patrons were there?
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
Let
Adult ticket = a
Child ticket = c
Total Tickets sold = 5200
c+a=5200
c=5200-a ..........(1)
Cost per adult ticket = 4.75
Cost per child ticket = 2.50
Total income from Adult tickets = 4.75 * a = 4.75a
Total income from Children tickets = 2.50 * c=2.50c
Total income = 20335
income from Adult tickets + income form children tickets = Total income
4.75a+2.50c=20335.........(2)
Put the value of c from (1) to above equation
4.75a+2.50(5200-a)=20335
4.75a+2.50(5200-a)=20335
4.75a+13000-2.5a=20335
2.25a=20335-13000
2.25a=7335
Divide by 2.25 both sides of above equation
2.25a/2.25=7335/2.25
a=3260
Put the value of a in (1)
c=5200-a ..........(1)
c=5200-3260
c=1940
Adult tickets sold or Adult patrons = 3260
Child ticket sold or Children present= 1940

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