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. (1 point)
To find out how much money the theater made from the sale of children's tickets, we need to calculate the total number of adult tickets sold and the cost of each children's ticket.
Given that 2/3 of the tickets sold were adult tickets, let's find the number of adult tickets sold:
Number of adult tickets = 2/3 * Total number of tickets
= 2/3 * 345
= 230 (rounded to the nearest whole number)
Now let's find the cost of each children's ticket. You mentioned that they cost 2/3 of the amount of adult tickets. Therefore:
Cost of each children's ticket = 2/3 * Cost of each adult ticket
= 2/3 * $13.95
= $9.30 (rounded to the nearest cent)
Since we know the number of adult tickets sold and the cost of each children's ticket, we can calculate the total amount of money made from the sale of children's tickets:
Total amount of money from children's tickets = Number of children's tickets * Cost of each children's ticket
= (Total number of tickets - Number of adult tickets) * Cost of each children's ticket
= (345 - 230) * $9.30
= 115 * $9.30
= $1,069.50 (rounded to the nearest cent)
Therefore, the theater made $1,069.50 from the sale of children's tickets.
The number of adult tickets sold was 345 tickets * (2/3) = <<345*(2/3)=230>>230 tickets.
The price of an adult ticket is $13.95 * 230 tickets = $<<13.95*230=3208.50>>3208.50
The price of a child ticket is (2/3)*$13.95 = $<<2/3*13.95=9.30>>9.30
The number of child tickets sold is 345 tickets - 230 tickets = <<345-230=115>>115 tickets
The money made from child tickets is 115 tickets * $9.30 = $<<115*9.30=1069.50>>1069.50
The theater made a total of $3208.50 + $1069.50 = $<<3208.50+1069.50=4278>>4278. Answer: \boxed{4278}.
Step 1: Calculate the number of adult tickets sold.
To find the number of adult tickets sold, multiply the total number of tickets sold (345) by the fraction that represents the proportion of adult tickets, which is 2/3.
Number of adult tickets sold = 345 * 2/3
Number of adult tickets sold = 230
Step 2: Calculate the cost of adult tickets.
To find the total cost of adult tickets, multiply the number of adult tickets sold (230) by the cost of each adult ticket ($13.95).
Total cost of adult tickets = 230 * $13.95
Step 3: Calculate the cost of children's tickets.
The cost of children's tickets is 2/3 of the amount of adult tickets, which means they cost 2/3 * $13.95.
Step 4: Calculate the number of children's tickets sold.
To find the number of children's tickets sold, subtract the number of adult tickets sold (230) from the total number of tickets sold (345).
Number of children's tickets sold = 345 - 230
Step 5: Calculate the total cost of children's tickets.
To find the total cost of children's tickets, multiply the number of children's tickets sold (115) by the cost of each children's ticket (2/3 * $13.95).
Step 6: Calculate the total money made from the sale of children's tickets.
To find the total money made from the sale of children's tickets, add the total cost of children's tickets to the total cost of adult tickets.
Total money made from the sale of children's tickets = Total cost of children's tickets + Total cost of adult tickets
Step 7: Round the answer to the nearest hundredth and add commas in appropriate places.
Provide the answer according to the instructions.