Answer: 341 children, 273 senior citizens and 291 adults attended the Family Arts Center.
Step-by-step explanation:
Let x represent the number of children that attended.
Let y represent the number of senior citizens that attended.
Let z represent the number of adults that attended.
The total number of tickets sold is 905. It means that
x + y + z = 905- - - -- - -- - - - - -1
The Family Arts Center charges $21 for adults, $13 for senior citizens, and $8 for children under 12 for their live performances on Sunday afternoon. This past Sunday, the paid revenue was $12,388. It means that
8x + 13y + 21z = 12388- - - - - - - - - -2
There were 50 more children than adults.. It means that
x = z + 50- - - - - - - - - -- - -3
Substituting equation 3 into equations 1 and 2, it becomes
z + 50 + y + z = 905
y + 2z = 905 - 50
y + 2z = 855
y = 855 - 2z- - - - - - - - - -4
8(z + 50) + 13y + 21z = 12388
8z + 400 + 13y + 21z = 12388
13y + 8z + 21z = 12388 - 400
13y + 29z = 11988- - - - - - - 5
Substituting equation 4 into equation 5, it becomes
13(855 - 2z) + 29z = 11988
11115 - 26z + 29z = 11988
- 26z + 29z = 11988 - 11115
3z = 873
z = 873/3
z = 291
x = z + 50 = 291 + 50
x = 341
y = 855 - 2z = 855 - 2(291)
y = 273
