Final answer:
By setting up a system of linear equations with variables representing the number of balcony and main level tickets sold, and solving these equations, it is determined that 183 balcony tickets and 242 main level tickets were sold. The provided answer choices do not match this correct solution, indicating an error in the question options.
Step-by-step explanation:
To determine how many balcony tickets and main level tickets were sold for the concert at Main Street Theater, we need to set up a system of equations based on the information provided:
- Total tickets sold: 425
- Balcony ticket price: $5
- Main level ticket price: $8
- Total receipts: $2,851
Let x represent the number of balcony tickets sold and y represent the number of main level tickets sold.
We can set up the following equations:
- x + y = 425 (total number of tickets)
- 5x + 8y = 2851 (total receipts from ticket sales)
By solving this system of equations, we can find the exact number of each type of ticket that was sold. Here's the solution step-by-step:
- Multiply the first equation by -5 to set up for elimination.
- Add the modified first equation to the second equation to eliminate the variable x.
- Solve for the variable y.
- Substitute the value of y into the first equation to solve for x.
Let's see how it works:
- -5(x + y = 425) → -5x - 5y = -2125
- (5x + 8y = 2851) + (-5x - 5y = -2125) → 3y = 726
- y = 726 / 3 → y = 242 (main level tickets)
- x + 242 = 425 → x = 425 - 242 → x = 183 (balcony tickets)
Therefore, the number of balcony tickets sold is 183 and main level tickets is 242. The correct answer to the question is not listed in the options provided, which indicates a possible typo or error in the question.