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. The combined cost of one advance ticket and one same-day ticket is $65. For one performance, 15 advance tickets and 35 same-day tickets were sold. The total amount paid for the tickets was $1675. 

What was the price of each kind of ticket?

Answer 1

One advance ticket plus one same-day ticket cost $65.

15 advance tickets plus 15 same-day tickets cost 15x$65=$975.

Add 20 same-day tickets and the total gate is $1675.

So 20 same-day tickets cost $1675-$975=$700.

Then one same-day ticket is $700/20=$35.

One advance ticket is $65-$35=$30.

Make sense?