SOLUTION: The Family Arts Center charges $22 for adults, $17 for senior citizens, and $8 for children under 12 for their live performances on Sunday afternoon. This past Sunday, the paid r

Algebra ->  Equations -> SOLUTION: The Family Arts Center charges $22 for adults, $17 for senior citizens, and $8 for children under 12 for their live performances on Sunday afternoon. This past Sunday, the paid r      Log On


   

Question 1115267: The Family Arts Center charges $22 for adults, $17 for senior citizens, and $8 for children
under 12 for their live performances on Sunday afternoon. This past Sunday, the paid
revenue was $12,980 for 856 tickets sold. There were 44 more children than adults. How
many children attended?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

$22 for adults, numbers be x
$17 for senior citizens, numbers be y
and $8 for children under 12 x+44
Total attendance
x+y+(x+44) =856
2x+y = 812....................(1)
the paid revenue was $12,980
22x+17y+(x+44)*8 = 12980
22x+17y+8x+352=12980
30x+17y=12628.................(2)

2 x + 1 y = 812 .............1


30 x + 17 y = 12628 .............2
Eliminate y
multiply (1)by 17
Multiply (2) by -1
34 x 17 y = 13804
-30 x -17 y = -12628
Add the two equations
4 x = 1176
/ 4
x = 294
plug value of x in (1)
2 x + 1 y = 812
588 + 1 y = 812
1 y = 224
y = 224
Ans x = 294
y = 224
294 adults
224 senior citizens
(294+44) children