The little town arts center charges $23 for adults, $13 for senior citizens, and $6 for children under 12 for their live performances on Sunday afternoon. This past Sunday, the paid revenue was $11,338 for 834 tickets sold. There were 41 more children that adults. How many children attended?

261 adults, 271 senior citizens, 302 children

Step-by-step explanation:

Let's define our variables

x: adults

y: senior citizens

z: children

From this "834 tickets sold" we have that

x+y+z=834 (1)

From this "There were 41 more children that adults" we have that

x+41=z (2)

From This "the paid revenue was $11,338" we have that

23x+13y+6z=11338 (3)

If we plug (2) in (1) and (3) we get:

x+y+x+41=834

2x+y=793

y=793-2x (4)

23x+13y+6 (41+x) = 11338

23x+13y+6x=11338-246

29x+13y=11092 (5)

plugging (4) in (5)

29x+13 (793-2x) = 11092

29x+10309-26x=11092

3x=783

x=261 adults (6)

(6) in (4)

y=793-2 (261) = 271 senior citizens

(6) in (2)

261+41=z

z=302 children