Final answer:
To solve the student's question, a system of equations is set up with two variables representing the number of adult and children's tickets. By using the substitution method, we find that 235 adult tickets and 415 children's tickets were sold.
Step-by-step explanation:
The student is asking a question related to algebra and systems of equations. They need to find out how many adult and children's tickets were sold when the total sales were $3,305, and a total of 650 tickets were sold with the knowledge that adult tickets cost $7 and children's tickets cost $4.
Let's define two variables: A for the number of adult tickets and C for the number of children's tickets. We can set up the following system of equations based on the given information:
- 7A + 4C = 3305 (equation for the total sales)
- A + C = 650 (equation for the total number of tickets)
To solve this system, we can use a method such as substitution or elimination. For example, we can solve the second equation for A (A = 650 - C) and substitute that into the first equation, giving us a single equation in one variable:
7(650 - C) + 4C = 3305
This simplifies to 4550 - 7C + 4C = 3305, which further simplifies to -3C = -1245. Dividing both sides by -3 gives us C = 415. With the number of children's tickets known, we can calculate the number of adult tickets as A = 650 - 415, giving A = 235.
Therefore, 235 adult tickets and 415 children's tickets were sold.