Final answer:
By setting up a system of equations and using the elimination method, we determined that 392 children's tickets were sold at the arts festival.
Step-by-step explanation:
The subject of this question is how to determine the number of children's admission tickets sold for a local performing arts festival by the Doniphan County Players. To find the answer, we can set up a system of equations based on the total number of tickets sold and the total revenue generated from those tickets.
Let x represent the number of adult tickets sold at $20 each and y represent the number of children's tickets sold at $12 each. We are given two equations based on the information in the question:
x + y = 824 (total tickets)
20x + 12y = $13,344 (total revenue)
Now we can solve this system of equations using either the substitution or elimination method. In this case, we will use the elimination method. Multiplying the first equation by 12, we get:
12x + 12y = 9,888
Subtract this from the second equation to eliminate y:
(20x + 12y) - (12x + 12y) = 13,344 - 9,888
8x = 3,456
Solving for x, we find:
x = 3,456 / 8
x = 432
Now, we can substitute x = 432 into the first equation to find y:
432 + y = 824
y = 824 - 432
y = 392
Therefore, 392 children's tickets were sold, which corresponds with option d.