SOLUTION: A stage theater sold tickets for $ 300. Senior citizens received a discount of 30%, and paid only $ 210. On the initial showing, the theater sold 250 tickets and registered a tota

Question 1171322: A stage theater sold tickets for $ 300. Senior citizens received a discount of 30%, and paid only $ 210. On the initial showing, the theater sold 250 tickets and registered a total of $ 66,000. How many of each type tickets were sold?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

First, a typical algebraic setup for solving the problem....

x = number of senior tickets
250-x = number of regular tickets

Total ticket sales was $66,000:

Solve for x using basic algebra; then use that value to find the numbers of each kind of ticket. I leave it to you to finish solving the problem by that method.

Here is an alternative method for solving "mixture" problems like this that I prefer, because (for me) I get to the answer faster and with less effort.

(1) Determine that the average ticket price, for $66,000 from 250 tickets, is $66000/250 = $264.
(2) Look at the three prices $210, $264, and $300 on a number line and use simple calculations to determine that $264 is 54/90 = 6/10 = 3/5 of the way from $210 to $300.
(3) That means 3/5 of the tickets were the higher priced tickets.

ANSWER: 3/5 of 250 tickets, or 150 tickets, were regular tickets; the other 100 tickets were senior tickets.

CHECK: 150(300)+100(210) = 45000+21000 = 66000

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