Final answer:
To find the number of children attending the show, we can set up a system of equations based on the given information. Solving this system of equations will allow us to determine the number of adults and children. Using this approach, we find that there were 529 children attending the show.
Step-by-step explanation:
To solve this problem, let's assign variables to represent the number of adults, senior citizens, and children attending the show. Let A represent adults, S represent senior citizens, and C represent children. We know that the cost of each ticket is $21 for adults, $16 for senior citizens, and $6 for children. We also know that the total revenue from the show was $12,635 and 910 tickets were sold. Finally, we know that there were 47 more children than adults at the showing.
Based on the given information, we can set up a system of equations to solve for the number of children attending:
1) A + S + C = 910 (equation representing the total number of tickets sold)
2) 21A + 16S + 6C = 12,635 (equation representing the total revenue)
3) C = A + 47 (equation representing the relationship between children and adults)
First, we can substitute equation 3 into equations 1 and 2:
A + S + (A + 47) = 910
21A + 16S + 6(A + 47) = 12,635
Simplifying these equations, we get:
2A + S = 863 -- equation 4
27A + 16S = 12,397 -- equation 5
We can now solve this system of equations using substitution or elimination. Let's use substitution:
From equation 4, we can express S in terms of A:
S = 863 - 2A
Substituting this expression for S in equation 5, we have:
27A + 16(863 - 2A) = 12,397
Expanding and simplifying this equation, we get:
27A + 13808 - 32A = 12,397
-5A + 13808 = 12,397
-5A = -2,411
A = 482.2
Since the number of adults must be a whole number, we can conclude that there were 482 adults attending the show.
Using equation 3, we can find the number of children:
C = A + 47 = 482 + 47 = 529
Therefore, there were 529 children attending the show.