Debra is buying prizes for a game at her school's fundraiser. The game has three levels of prizes, and she has already bought the second and third prizes. She wants the first prize to be nice enough to attract people to the game. The game's manufacturer has supplied her with the probabilities of winning first, second, and third prizes. Tickets cost $3 each, and she wants the school to profit an average of $1 per ticket. How much should she spend on each first prize? (Give your answer to the nearest cent.)

Question

Prize Cost of Prize Probability
1st $ 0.15

2nd $1.28 0.30

3rd $0.70 0.45

Answer 1

.15x + .3(1.28) + .45(.70) + 1 = 3

I got x = 8.67

Check:
expected value (what you have to pay out)
= .15(8.67) + .3(1.28) + .45(.7) = 1.995
or $2.00, but each ticket costs $3, so they make $1 per ticket