A business purchases an item for $32.32. They want to make a gross profit margin of 27% on the item. What do they need to price the item at?
Selling Price = $[?]
Round to the nearest cent.
Answer (2)
Define the cost (C) as $32.32 and the desired profit margin (P) as 27% (0.27).
Use the gross profit margin formula: P = S S − C , where S is the selling price.
Substitute the given values and solve for S: 0.27 = S S − 32.32 which simplifies to S = 0.73 32.32 .
Calculate S and round to the nearest cent: S ≈ $44.27 .
Explanation
Problem Analysis The business purchased an item for $32.32 and wants to achieve a gross profit margin of 27% on the item. Our goal is to determine the selling price that achieves this profit margin. Let's define the cost of the item as C = $32.32, the desired gross profit margin as P = 27% = 0.27, and the selling price as S, which we want to find.
Understanding Gross Profit Margin The gross profit margin is calculated as the profit divided by the selling price. In equation form, this is: P = S S − C We are given P = 0.27 and C = $32.32. We need to solve for S.
Setting up the Equation Substitute the given values into the equation: 0.27 = S S − 32.32 Now, we solve for S. Multiply both sides by S: 0.27 S = S − 32.32 Subtract S from both sides: − 0.73 S = − 32.32 Divide both sides by -0.73: S = − 0.73 − 32.32 = 0.73 32.32
Calculating the Selling Price Now, we calculate the value of S: S = 0.73 32.32 ≈ 44.27397 We need to round this to the nearest cent, which gives us $44.27.
Final Answer Therefore, the business needs to price the item at $44.27 to achieve a 27% gross profit margin.
Examples
Understanding profit margins is crucial in business. For example, if a store buys a batch of T-shirts for $10 each and wants to make a 30% profit margin, they need to calculate the selling price. Using the formula, if C = $10 and P = 0.30, then 0.30 = (S - 10) / S. Solving for S gives S = $14.29. This ensures the store covers its costs and makes the desired profit on each T-shirt. This calculation helps in setting competitive prices while maintaining profitability.
The selling price that the business needs to set for the item is $44.27 to achieve a gross profit margin of 27%. This was calculated using the formula for gross profit margin and rearranging the equation to solve for the selling price. By dividing the cost of the item by (1 - desired profit margin), we get the final selling price.
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