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?

Accepted Solution

Answer:261 adults, 271 senior citizens, 302 childrenStep-by-step explanation:Let's define our variablesx:  adultsy: senior citizensz: childrenFrom this "834 tickets sold" we have thatx+y+z=834 (1)From this "There were 41 more children that adults" we have thatx+41=z (2)From This "the paid revenue was $11,338" we have that23x+13y+6z=11338 (3)If we plug (2) in (1) and (3) we get:x+y+x+41=8342x+y=793 y=793-2x (4)23x+13y+6(41+x)=1133823x+13y+6x=11338-24629x+13y=11092 (5)plugging (4) in (5)29x+13(793-2x)=11092 29x+10309-26x=110923x=783x=261 adults (6)(6) in (4)y=793-2(261)=271 senior citizens(6) in (2)261+41=zz=302 children