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# 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?

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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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