First, we need to calculate how many tickets were sold to adults. Since 2/3 of the tickets sold were to adults, we can find the number of adult tickets sold by multiplying the total tickets by 2/3:
\[ \text{Adult tickets} = \frac{2}{3} \times 345 = 230 \]
Next, we can calculate how many tickets were sold to children by subtracting the number of adult tickets from the total tickets sold:
\[ \text{Children tickets} = 345 - 230 = 115 \]
Now, we know the price of an adult ticket is $13.95. The price of a children's ticket is 2/3 of the adult ticket price:
\[ \text{Children's ticket price} = \frac{2}{3} \times 13.95 \]
Calculating the children's ticket price:
\[ \text{Children's ticket price} = \frac{2 \times 13.95}{3} = \frac{27.90}{3} = 9.30 \]
Now we can find the total revenue from selling children's tickets by multiplying the number of children's tickets sold by the price of a children's ticket:
\[ \text{Total revenue from children's tickets} = 115 \times 9.30 \]
Calculating this gives:
\[ \text{Total revenue from children's tickets} = 1069.50 \]
Finally, rounding to the nearest hundredth, the theater made $1069.50 from the sale of children's tickets.
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