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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Kiara has a home-based business making and selling scented soaps. She intially spent to purchase soap-making equipment, and the materials for each pound of soap cost . Kiara sells the soap for per pound. Eventually, she will sell enough soap to cover the cost of the equipment. How much soap will that be? What will be Kiara's total sales and costs be?Once Kiara sells _____ pounds of soap, her sales and costs will both be _____.
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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Kiara has a home-based business making and selling scented soaps. She intially spent to purchase soap-making equipment, and the materials for each pound of soap cost . Kiara sells the soap for per pound. Eventually, she will sell enough soap to cover the cost of the equipment. How much soap will that be? What will be Kiara's total sales and costs be?Once Kiara sells _____ pounds of soap, her sales and costs will both be _____.
- Define Variables: Define the variables and write the equations.Let be the number of pounds of soap Kiara sells.Kiara's total cost () includes the initial equipment cost and the cost of materials per pound of soap. initial equipment cost (cost per pound of soap )Kiara's total sales () are based on the selling price per pound of soap. selling price per pound of soap
- Set Equations: Set up the equation to find the break-even point where sales equal costs.
- Solve Equation: Solve for using substitution or elimination.
- Calculate Sales and Costs: Calculate the total sales and costs when Kiara sells pounds of soap.Total sales (S) when :Total costs (C) when :
- Verify Break-even Point: Verify that the total sales and costs are equal at the break-even point.
