Suppose that there are two types of tickets to a show: advance and same day.

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 $25. For one performance there were 35 tickets sold in all, and the total amount paid for them was $975. How many tickets of each type were sold?

Answer 1

When you have two unknowns (advanced tickets and same day tickets) you must create two equations and solve the system.

the cost equation is 30a+25s=975

the ticket equation a+s=35

The quickest way to solve this is by substitution

Solve for “a” or “s” in the second equation. I will solve for “a” which is a=35-s

Plug in

30(35-s)+25s=975

1050-30s+25s=975

1050-5s=975

1050-975=5s

75=5s

s=15

Then plug in 15 for s in the original equation a+s=34 or a=35-s then a=20

20 advance tickets

15 same day tickets