Please show work
The little town arts center charges $21 for adults, $17 for senior citizens and $8 for children under 12 for their lfe performance on sunday. On sunday the revenue paid wa $13,274 for 886 tickets sold. There were 47 more children than adults. How many children attended?
children - c
adults - a
seniors - s
8c + 17s + 21a = 13274
c = a+47
a+c+s = 886
s = 886-a-c
= 886 - a - (a+47)
= 839 - 2a
sub back
8(a+47) + 17(839-2a) + 21a = 13274
solve for a, from there you can find c
283
Let's assume the number of adults who attended the live performance on Sunday is "A".
According to the given information, the number of children under 12 is 47 more than the number of adults. Hence, the number of children can be represented as "A + 47".
The revenue from each adult ticket is $21, so the total revenue from the adult tickets is 21A.
Similarly, the revenue from each senior citizen ticket is $17, and the number of senior citizens is not given. Therefore, we'll ignore the revenue from senior citizens for now.
The revenue from each child ticket is $8, so the total revenue from the child tickets is 8(A + 47).
The total revenue from all the tickets sold is $13,274. Therefore, we can set up the equation:
21A + 8(A + 47) = 13,274
Now, let's solve this equation step-by-step:
21A + 8A + 376 = 13,274
29A + 376 = 13,274
29A = 13,274 - 376
29A = 12,898
Divide both sides of the equation by 29:
A = 12,898 / 29
A ≈ 445.10
Since the number of adults cannot be a decimal, we can take the closest whole number, which is 445 (rounded down).
Now, let's find the number of children:
Number of children = A + 47 = 445 + 47 = 492
Therefore, there were 492 children who attended the live performance on Sunday.
To find the number of children who attended the performance, we need to solve the given problem step by step.
Let's assume:
Let the number of adults attending the performance be A.
Let the number of senior citizens attending the performance be S.
Let the number of children attending the performance be C.
Now, we have some information given in the problem:
1) The little town arts center charges $21 for adults, $17 for senior citizens, and $8 for children under 12 for their life performance on Sunday.
2) On Sunday, the revenue paid was $13,274 for 886 tickets sold.
3) There were 47 more children than adults.
From the given information, we can form three equations:
Equation 1: Revenue earned from adults + Revenue earned from senior citizens + Revenue earned from children = Total revenue.
21A + 17S + 8C = 13274
Equation 2: Number of adults + Number of senior citizens + Number of children = Total tickets sold.
A + S + C = 886
Equation 3: Number of children = Number of adults + 47.
C = A + 47
Now, we can solve these equations to find the values of A, S, and C:
We can rewrite Equation 2 by substituting Equation 3 into it:
A + S + A + 47 = 886
2A + S = 839
Now, we can solve these equations by elimination or substitution methods. For simplicity, we will use the substitution method here:
Substitute the value of S from Equation 2 into Equation 1:
21A + 17(839 - 2A) + 8C = 13274
21A + 14263 - 34A + 8C = 13274
-13A + 8C = -981
Now, we can substitute the value of C from Equation 3 into the last equation:
-13A + 8(A + 47) = -981
-13A + 8A + 376 = -981
-5A = -1357
A = 271
Substituting the value of A into Equation 3:
C = 271 + 47
C = 318
Therefore, there were 318 children attended the performance.