Your first assignment as a "math advisor" is to work with Wanda, the new manager of the "Graceland Guanacos" hockey team.

A new season is about to begin, and Wanda is thinking of making some changes to the team she's just bought. When she took over, the team was charging $15 per ticket. She is thinking of raising the ticket price by some dollar amount "x". Right now, a typical Guanacos game attracts 500 fans, but you warn Wanda that more expensive tickets would mean fewer fans.

You do some market research, surveying many Guanacos fans after games. You ask how expensive tickets could get before they'd stop coming to games.

You learn that, in general, each $1 increase means that 20 fewer fans would buy tickets.

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1. Creating the Equation

a) Create an algebraic expression to represent ticket price after some price increase "x" has been added.

b) Create an algebraic expression to represent the number of fans who would attend the game after some price increase "x" has been added.

c) The revenue R(x) from ticket sales can be found by multiplying the ticket price by the number of fans who buy tickets. Given this, find an expression for the revenue, R(x), for a given price increase, x.

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2. Converting the Equation

a) You generated a quadratic equation in 1c). In which form is this equation written?

b) Convert this form to two forms of quadratic equations

c) Restate your equation here in itsthree forms. For each form of the equation, explain what useful information can be gathered easily from that form.

d) From these equations, what's the maximum revenue that Wanda can make from one game's ticket sales? What would she have to charge per ticket?

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3. Investing the Money (7 marks)

Every month, the team plays 9 games, and they play for a 7-month season. At the end of each month, Wanda has to take $67500 and put it towards the team's expenses.

Before Wanda raised the ticket price, tickets were bringing in exactly $67 500 a month. Now, thanks to your math skills, she is going to raise the ticket price to the point where she'd earn maximum profit. Wanda suggests taking that extra money and storing it in a bank account for emergencies or special projects.

Knowing the value of compound interest, you suggest that Wanda take all her profits and deposit them each month into a savings account. You suggest she do this in an account which earns 2%/a compounded monthly.

Wanda makes these deposits each month for the seven-month season. For the last five months of the year, the money sits in the account untouched (no more deposits), but still earning interest. At the end of all of this, how much extra money has your helpful suggestion earned the team?