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.
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 = ...
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?".