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:

two pairs of adjacent sides are of equal length. this implies that one diagonal divides the kite into congruent triangles, and so the angles between the two pairs of equal sides are equal in measure. it also implies that the diagonals are perpendicular.

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step-by-step explanation: