A movie theater sold a total of 520 adult and child tickets on a certain day. The theater sold 2.25 times as many adult tickets as child tickets. Each adult ticket cost $9 and each child ticket cost $2. How much revenue did the theater generate in ticket sales that day?

Answer 1

For every child ticket, 2.25 adult tickets were sold.
This is the same as
For every 4 child tickets sold, 9 adult tickets were sold, for a total of 4*2+9*9=$89.
Number of sets of sets (4+9) sold = 520/13=40
Total amount = 40*$89=$3560

Alternatively, using algebra,
A=number of adult tickets sold, then
A/2.25 = number of child tickets sold.
Therefore
A+A/2.25=520
A=520/(1+1/2.25)=520*(2.25/3.25)=360
Number of child tickets sold = 520-350= 160
Total revenue
=360*9+160*2
=3240+320
=$3560