Final answer:
After calculating correctly, the number of child tickets sold is 40, which does not match any of the provided options (20, 25, 30, or 35). This suggests that either an error is present in the problem statement or the answer choices provided.
Step-by-step explanation:
To determine how many child tickets were sold at the movie theatre, where child admission is $6.10 and adult admission is $9.70, and on Friday, twice as many adult tickets as child tickets were sold for a total sales of $1020.00, we need to set up a system of equations.
Let's denote the number of child tickets sold as c and the number of adult tickets sold as a. According to the problem, there were twice as many adult tickets sold as child tickets, which we can write as:
a = 2c
The total revenue generated from selling adult and child tickets is given by:
6.10c + 9.70a = 1020
Substituting the first equation into the second gives:
6.10c + 9.70(2c) = 1020
Now, we combine like terms:
6.10c + 19.40c = 1020
25.50c = 1020
Dividing both sides by 25.50 to solve for c:
c = 1020 / 25.50
c = 40
However, this answer is not available in the options given; thus, we must have made a mistake. Let's correct the math:
6.10c + 19.40c = 1020
Combining like terms correctly:
6.10c + 19.40c = 25.50c
25.50c = 1020
c = 1020 / 25.50
c = 40
It seems we've made another error as this is still incorrect and not one of the options provided. Let's retry the calculation:
c = 1020 / 25.50
c = 40
After carefully re-checking, the calculation appears correct, suggesting that a mistake has been made in the problem statement or the answer choices provided. It may be necessary to communicate with the student or the entity responsible for the question to resolve this inconsistency. In reality, given the correct arithmetic, 40 child tickets were sold, which does not match any of the provided answer options of 20, 25, 30, or 35.