The movie theater sold 345 tickets to a show. If 2/3 of the tickets sold were adult tickets, which cost $13.95 each, how much money did the theater make from the sale of children's tickets if they cost 2/3 of the amount of adult tickets? Answer with a dollar amount rounded to the nearest hundredth, placing commas in appropriate places.
First, let's calculate the number of adult tickets sold. Since 2/3 of the tickets were adult tickets, we have:
Adult tickets sold = (2/3) * 345
To find how much money was made from adult tickets, multiply the number of adult tickets by the price per adult ticket ($13.95):
Money from adult tickets = Adult tickets sold * $13.95
But we want to find out the money made from children's tickets. First, to calculate the number of children's tickets sold, we subtract the number of adult tickets from the total number of tickets:
Children's tickets sold = Total tickets - Adult tickets sold
Also, since a children's ticket costs 2/3 of an adult ticket, we have:
Price of children's ticket = (2/3) * $13.95
Then we can compute the money made from children's tickets by multiplying the number of children's tickets by the price of each children's ticket:
Money from children's tickets = Children's tickets sold * Price of children's ticket
Let's do the math step by step:
1. Adult tickets sold = (2/3) * 345 = 230
2. Children's tickets sold = 345 - 230 = 115
3. Price of children's ticket = (2/3) * $13.95 = $9.30 (since 13.95 divided by 3 equals 4.65 and then multiplied by 2)
4. Money from children's tickets = 115 * $9.30
Now let's do this final calculation:
Money from children's tickets = 115 * $9.30 = $1,069.50
So the theater made $1,069.50 from the sale of children's tickets, rounded to the nearest hundredth.