Solving a value mixture problem

Question

Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $35 and same-day tickets cost $40. For one performance, there were 55 tickets sold in all, and the total amount paid for them was $2025. How many tickets of each type were sold?

Answer 1

A + S = 55

35A + 40S = 2025 multiply 1st equation by 35 and subtract from the 2nd equation

35A + 35S = 1925

5 S = 100

S = 20 same day tickets

A = 55-20 = 35 advance tickets

35(35) + 40(20 = 1225+800 = 2025