Question

he 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)

Answer 1

First, we need to determine how many adult tickets were sold. According to the problem, 2/3 of the tickets sold were adult tickets.

Total tickets sold = 345
Adult tickets sold = $\frac{2}{3}\times 345$

Calculating the number of adult tickets sold:

$$\text{Adult tickets sold}=\frac{2}{3}\times 345=230$$

Next, we can find the number of children's tickets sold. Since adult tickets sold are 230:

$$\text{Children's tickets sold}=345-230=115$$

Next, we calculate the price of a children's ticket. The cost of an adult ticket is $13.95, and a children's ticket costs $\frac{2}{3}$ of the cost of an adult ticket.

Calculating the cost of a children's ticket:

$$\text{Cost of children's ticket}=\frac{2}{3}\times 13.95$$

Calculating the value:

$$\text{Cost of children's ticket}=\frac{2\times 13.95}{3}=\frac{27.90}{3}=9.30$$

Now, we can calculate the total revenue from children's tickets:

$$\text{Total revenue from children's tickets}=\text{Children's tickets sold}\times \text{Cost of children's ticket}$$

Calculating the total revenue:

$$\text{Total revenue from children's tickets}=115\times 9.30=1069.50$$

Thus, the theater made $1,069.50 from the sale of children’s tickets.