Option A Option B

60/40 Raffle Raffle tickets are sold for $4 each. The person whose ticket is drawn wins 40% of the total amount collected from ticket sales. The remaining 60%goes to the charity

Battle of the Bands The committee rents the local community theatre to hold a battle of the bands contest. The theatre always charges the same fixed rental fee. Two other schools ran similar fundraisers earlier in the year. One school sold 100 tickets and raised $50 for charity. The second school sold 300 tickets and raised $1050 for charity. Each of the schools charged the same price for tickets.

For Option A, let x represent the number of raffle tickets sold and y represent the amount that goes to the charity. Write an algebraic equation to model the amount raised for charity by Option A.

a) For Option B, let p represent the price of one ticket and r represent the fixed rental fee at the community theatre. Use the information about the fundraisers held by the other two schools to determine the fixed rental fee and the ticket price.

b) Use your answer from part a) Let x represent the number of tickets sold for the battle of the bands and y represent the amount raised for charity. Write an algebraic equation to model the amount raised for charity by option B

a) Write and solve a system of linear equations to determine the number of tickets that must be sold for options A and B to raise the same amount of money.

b) Under what conditions would you recommend using Option A? Option B?

a) Suppose 200 tickets are sold. Which option would raise more money? How much more?

b) Without calculating the difference, will the difference between the amount raised using each option increase or decrease if only 100 tickets are sold? Explain your reasoning.