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?

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?

Question
Equations and inequalities
asked 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?

Answers (1)

2021-02-09

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):
\(c= 3800-a\)
Substitute (3) to (2) and solve for a: \(9a + 6.50(3800 - a) = 30495\)
\(9a + 24700 - 6.50a = 30495\)
\(2.50a = 5795\)
\(a= 2318\)
Solve for c using (3): \(c=3800 - 2318\)
\(c= 1482\)
So, there were 2318 adult tickets and 1482 children’s tickets sold.

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