Susie wants to start making and selling bracelets. Her costs are the large sum of money that includes her initial investment and the cost of materials for each bracelet. She has already planned how much she is going to sell her bracelets for. Explain how Susie can set up a system of equations to predict when she will start to make a profit.

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Susie wants to start making and selling bracelets. Her costs are the large sum of money that includes her initial investment and the cost of materials for each bracelet. She has already planned how much she is going to sell her bracelets for. Explain how Susie can set up a system of equations to predict when she will start to make a profit.

Mathematics
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let initial investment =x cost of material =y number of bracelets=z then selling price of each \[>\frac{ x+y }{ z }\]

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Her cost is the initial investment + the amount it takes for each bracelet multiplied by the number of bracelets. Write that equation Her income is the amount she sells each bracelet for multiplied by the number of bracelets. Write that equation. When Cost = Income, she is at break even. When Income exceeds Cost, she is making a profit.
The initial cost is f (a fixed amount) The cost of materials per bracelet is m, so fr x bracelets, her cost is mx The total cost is \(C = mx + f\) She sells each bracelet for p, the price of a bracelet, so she receives mp in sales. Her income from sales is \(I = mp\) When I = C, she breaks even. When I > C she makes a profit.

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