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 20 same-day tickets were sold. The total amount paid for the tickets was $1150. What was the price of each kind of ticket?

Advance tickets cost $30; same-day tickets cost $35.

Step-by-step explanation:

Let a = the cost of an advance ticket

and s = the cost of a same-day ticket

We have two conditions:

(1) a + s = 65

(2) 15a + 20s = 1150

Subtract a from each side of (1) (3) s = 65 - a

Substitute (3) into (2) 15a + 20 (65 - a) = 1150

Distribute the 20 15a + 1300 - 20a = 1150

Combine like terms 1300 - 5a = 1150

Subtract 1300 from each side - 5a = - 150

Divide each side by - 5 (4) a = 30

Substitute (4) into (1) 30 + s = 65

Subtract 30 from each side s = 35

Advance tickets cost $30; same-day tickets cost $35.

Check:

(1) 30 + 35 = 65 (2) 15 * 30 + 20 * 35 = 1150

65 = 65 450 + 700 = 1150

1150 = 1150