Solving a value mixture problem using a system of linear equations

Question

Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $30

 and same-day tickets cost $35 for one performance, there were 55

 tickets sold in all, and the total amount paid for them was $1775. How many tickets of each type were sold?

Answer 1

30 advance tickets and 25 same day tickets were sold

30(30 + 25(35) = 900 + 875 = 1775

A + S = 55 Equation I

30A + 35S = 1775 Equation II

multiply Equation I by 30

30A + 30S = 1650 Equation III

subtract Equation III from Equation II to get

5S = 125

divide both sides by 5

S = 125/5 = 25 same day tickets

A= 55-25 = 30 advance tickets