As part of a school fundraising event, Jamie buys \(x\) boxes of snacks for a total of $180. She plans to sell each box at a profit of 80 cents.
Write, in terms of \(x\), an expression for the price, in dollars, Jamie paid for one box.[1]
Hence, write an expression for her selling price, in dollars, of one box.[1]
Jamie managed to sell all except 15 of the boxes and collected $171 from his sales. Form an equation in \(x\), and show that it simplifies to \(4x^2-15x-13500=0\).[3]
Showing your working clearly, solve the equation in (b) and calculate the selling price of 1 box of snacks.[3]
Jamie considers increasing her selling price by $0.25 per box for the remaining 15 boxes. Would this allow her to make a profit overall? Justify your conclusion with mathematical calculations.[2]
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