Question

Suppose there are two types of tickets to a show: advance and same-day. Advance tickets cost $40 and same-day tickets cost $30. For one performance, there were 65 tickets in all, and the total amount paid for them was $2200. How many tickets of each type were sold?

Answer 1

Advance tickets: represented by x

Same-day tickets: represented by y

you can model this using a system of equations

x + y = 65

40x + 30y = 2200

then you have to get either the x or y value equivalent in both equations

40(x + y = 65)

40x + 40y = 2600

so the new equations are 40x + 40y = 2600 and 40x + 30y = 2200

then you can solve by using elimination

40x + 40y = 2600

-(40x + 30y = 2200)

10y = 400

y = 40

substitute y back into the first equation

x + 40 = 65

x = 25