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7 March, 06:05

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?

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  1. 7 March, 06:34
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    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
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