At a recent production of A Comedy of Errors, the Community Theater brought in a total of $30,495 in revenue. If adult tickets were $9 and children's tickets were $6.50, how many tickets of each type were sold if 3800 tickets in all were sold?

ediculeN

ediculeN

Answered question

2021-02-08

At a recent production of A Comedy of Errors, the Community Theater brought in a total of $30,495 in revenue. If adult tickets were $9 and children's tickets were $6.50, how many tickets of each type were sold if 3800 tickets in all were sold?

Answer & Explanation

2k1enyvp

2k1enyvp

Skilled2021-02-09Added 94 answers

Let с be the number of children’s tickets and 2 be the number of adult tickets sold.
Set up equations.
3800 tickets were sold, so we can write: a+c=3800
The total revenue is $30495, so we can write:
9a+6.50c=30495
Solve by substitution. Using (1), we solve for c to obtain (3):
c=3800a
Substitute (3) to (2) and solve for a: 9a+6.50(3800a)=30495
9a+247006.50a=30495
2.50a=5795
a=2318
Solve for c using (3): c=38002318
c=1482
So, there were 2318 adult tickets and 1482 children’s tickets sold.

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