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 for 905 tickets sold. There were 50 more children than adults. How many children attended? Summarize your answer in a complete sentence.

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

step-by-step explanation: