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?
Accepted Solution
A:
Answer: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