the little town arts center charges $21 adults, $14 seniors, and $6 for children under 12 for their live performances on sunday afternoon. This past sunday, the paid revenue was $9486 for 718 tickets sold. there were 44 more children than adults. How many children under 12 attended?
steve can you explain little bit for me please so i can understand how you got these answers
choises are:
258
214
246
248
To solve this problem, we need to set up a system of equations based on the given information.
Let's assign variables to the unknowns:
Let A be the number of adults.
Let S be the number of seniors.
Let C be the number of children under 12.
Based on the information given in the question, we can set up the following equations:
Equation 1: A + S + C = 718 (The total number of tickets sold is 718)
Equation 2: 21A + 14S + 6C = 9486 (The total revenue from ticket sales is $9486)
We also know that there were 44 more children than adults, so we can set up another equation using this information:
Equation 3: C = A + 44 (44 more children than adults)
Now we can solve the system of equations to find the values of each variable.
First, let's solve Equation 3 for A:
C = A + 44
A = C - 44
Substituting this into Equation 1:
(C - 44) + S + C = 718
2C + S = 762 ----(Equation 4)
Now, substitute the value of A from Equation 3 into Equation 2:
21(A) + 14S + 6C = 9486
21(C - 44) + 14S + 6C = 9486
21C - 924 + 14S + 6C = 9486
27C + 14S = 10410 ----(Equation 5)
We now have a system of two equations (Equations 4 and 5) with two variables (C and S). We can solve this system using substitution or elimination.
Let's use the substitution method, solve Equation 4 for S:
2C + S = 762
S = 762 - 2C
Substitute this value of S into Equation 5:
27C + 14(762 - 2C) = 10410
27C + 10668 - 28C = 10410
-C = 10410 - 10668
-C = -258
C = 258
Therefore, there were 258 children under 12 who attended the performance on Sunday afternoon.
a+s+c = 718
21a+14s+6c = 9486
c = a+44
a=214
s=246
c=258