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.