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A school dance sold 2 types of tickets: one for freshman/sophomores (9th/10th graders), and one for juniors/seniors (11th/12th graders). The freshman/sophomore tickets cost $8, and the junior/senior tickets cost $6. They sold a combined total of 525 tickets, and earned a total of $4600. How many tickets of each type did the school sell? Write and show all algebra work; you cannot use graphing to solve this.

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sqdancefan

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Answer:

  • freshman/sophomore: 725
  • junior/senior: -200

Step-by-step explanation:

It is convenient to let a variable represent the number of the highest-price tickets sold. We'll use x for that. Then the number of lower-price tickets sold is 525 -x and the total revenue is ...

  8x +6(525 -x) = 4600

  2x = 1450 . . . . . . . . . . . . subtract 3150

  x = 725

  525 -x = -200

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The school sold 725 freshman/sophomore tickets and -200 junior/senior tickets.

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Comment on the question

There is apparently an error in the question somewhere. The average revenue per ticket is ...

  $4600/525 ≈ $8.76

You cannot sell $6 and $8 tickets and earn more than $8 per ticket sold. (Average revenue must be between $6 and $8 per ticket.)

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If we assume a typo in revenue, and that it should be $3600, then the sales will be 225 freshman tickets and 300 senior tickets.

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