System of equations word problem

Question

Tickets to a 3D movie cost $12.50 for adults and $8.50 for children. The

theater can seat up to 260 people. A total of $1734 was collected in ticket

sales for the 7:15 PM show in which only 60% of the tickets were sold.

a. Write equations that represent this information.

b. Solve the equations to find how many adults and how many children

were in the theater.

Answer 1

12.5a +8.5c= 1734

a + c = .6(260) = 156

8.5a +8.5c =8.5(156

4a = 1734-8.5(156)

a = 433.5 -8.5(39)

= 433.5 -331.5

= 102 adults

c= 54 children

12.5(102)+8.5(54)

=1070+267.5+392+24.5

=1275+459

= 1734