Final answer:
By setting up a system of equations with two variables representing the number of adult and child tickets sold, and using the elimination method to solve it, it's determined that there are 137 adults and 113 children at the show.
Step-by-step explanation:
We have been given that the total revenue from ticket sales is $4,846, and the auditorium has a total of 250 seats. Adult tickets cost $23 each, and child tickets cost $15 each.
To find out how many adults and children are in attendance, we need to set up a system of equations and solve for the two variables representing the number of adults and children.
Let A be the number of adult tickets sold, and C be the number of child tickets sold. We can then establish the following system of equations based on the information provided:
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- A + C = 250 (since the total number of seats is 250)
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- 23A + 15C = 4846 (total revenue from ticket sales)
Now we need to solve this system of equations. We can use substitution or elimination methods. For this explanation, let's use the elimination method:
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- Multiply the first equation by 15 (the price of a child ticket) to eliminate C:
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- 15A + 15C = 3750
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- Subtract this new equation from the second equation to eliminate C and solve for A:
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- 23A + 15C - (15A + 15C) = 4846 - 3750
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- 8A = 1096
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- A = 137
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- Plug the value of A back into the first equation to solve for C:
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- 137 + C = 250
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- C = 250 - 137
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- C = 113
Therefore, there are 137 adults and 113 children in attendance at the show.