The starving actors guild holds its annual winter arts festival in hopes of raising $13,344 by selling 824 tickets. the guild charges $20 for adult admission tickets and $12 for childrens admission tickets. in order to meet the goal, how many of each type of the tickets need to be sold?

A + c = 824                             represents number of tickets to sell
20a + 12c = 13,344                represents cost of each type of ticket

multiply equation 1 by -12 to cancel the variable 'c' and solve for 'a'

-12(a + c = 824)

-12a - 12c = - 9888
 20a + 12c = 13,344         add equations together

    8a          = 3456           divide both sides by 8
     a = 432

To find children's tickets substitute adult numbers back into equation 1.
a + c = 824
432 + c = 824
subtract 432 from both sides
c = 392

adult 432, children 392