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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?

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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

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