Write a system of equations to solve the problem.
A local theater sells out for their show. They sell at 500 tickets for a total purse of $8,010.00.
The tickets were priced at $15.00 for students, $12.00 for children, and $18.00 for adults. If the band sold three times as many adult tickets as children's tickets, how many of each type were sold?
Let s represent the number of student tickets, c represent the number of child tickets, and a represent the number of adult tickets.
The given information creates the following system of equations:
1) s + c + a = 500 (Total number of tickets sold is 500)
2) 15s + 12c + 18a = 8010 (Total sales is $8,010)
3) a = 3c (Three times as many adult tickets sold as child tickets)
This system of equations can be used to find the number of each type of ticket sold.