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Statistics Project: Raffle Ticket Prices

Tina is offering raffle tickets to 300 co-workers for a very worthy cause, giving each a chance to win \$800 for the price of \$5, or a chance to win \$4000 for the price of \$20. Tina plans to cell all the tickets and be able to pay off the one winning ticket and still make \$1700 for the cause.

How many tickets must Tina sell at each price? Are these prices fair?

Please see attached file for full problem description.

Solution Preview

Let x be the number of tickets at the \$5 price, and let y be the number of tickets at the \$20 price. There are 300 total tickets (first equation), and the profit should be at least \$1700 after paying out the prize (second equation; the maximum prize is \$4000, so Tina needs to make \$5700). The way I understand the contest to work is that only one ticket is drawn. If it was a \$5 ticket, the person wins \$800, and if it was a \$20 ticket, the person wins \$4000.

x + y = 300
5x + 20y = 1700 + 4000 = ...

Solution Summary

The solution demonstrates how to solve a system of equations to answer the question "How many tickets must Tina sell at each price?". It uses probabilities and expected values to answer the question "Are these prices fair?".

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