San pablo is having a festival. tickets for children under 12 cost $2, adult tickets are $6 and senior citizen tickets are $3. one sixth of the tickets sold were children’s tickets. the 40 senior citizens with tickets sat in the shade under the trees and watched the children play. half the people attending the festival purchased adult tickets. how much money was collected from ticket sales?

The total of tickets sold would be 100% or 1, so we have 1/6 of total tickets for kids and 1/2 of total of tickets for adults, for finding the part of tickets sold for seniors we calculate: 1/6 + 1/2 + x = 1 here x is the part of tickets for seniors.
Solve for x: x=1/3.
Now let total of tickets be "T", we know the amount of tickets sold for seniors (40) so we can say: 1/3*T = 40, solve for T and get T = 40*3 = 120 tickets sold.
Finally we can calculate the money collected from tickets sold multiplying the cost*the part of tickets sold for each group*120 and add all of them, this is:
$2*1/6*120 + $6*1/2*120 + $3*1/3*120 = $40 + $360 + $120 = $520
The money collected from ticket sales is: $520