A business purchases an item for $56.78. They want to make a gross profit margin of 33% 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 = $56.78 and the desired profit margin P = 0.33 .
Use the gross profit margin formula: P = S S − C .
Rearrange the formula to solve for the selling price: S = 1 − P C .
Substitute the values and calculate: S = 1 − 0.33 56.78 = $84.75 . The final answer is 84.75
Explanation
Understanding the Problem Let's break down this problem. We're given the cost of an item and the desired gross profit margin. Our goal is to find the selling price that achieves this profit margin.
Identifying Knowns and Unknowns We know the cost of the item, which we'll call C , is $56.78 . The desired gross profit margin, which we'll call P , is 33% or 0.33 . We want to find the selling price, which we'll call S .
Stating the Formula The formula for gross profit margin is: P = S S − C where:
P is the gross profit margin,
S is the selling price,
C is the cost.
Rearranging the Formula We need to rearrange the formula to solve for S . Here's how we do it:
Multiply both sides by S : P × S = S − C
Rearrange to isolate S terms: PS = S − C
Move all S terms to one side: C = S − PS
Factor out S : C = S ( 1 − P )
Divide by ( 1 − P ) to solve for S : S = 1 − P C
Calculating the Selling Price Now, we plug in the values we know:
S = 1 − 0.33 56.78
S = 0.67 56.78
S = 84.74626865671642
Rounding to the nearest cent, we get S = 84.75 .
Final Answer Therefore, the business needs to price the item at $84.75 to achieve a 33% gross profit margin.
Examples
Imagine you're running a lemonade stand. Each cup of lemonade costs you $0.50 to make (lemons, sugar, water). You want to make a 50% profit margin on each cup. Using the same formula, you'd calculate your selling price as S = 0.50/ ( 1 − 0.50 ) = 0.50/0.50 = $1.00 . So, you'd sell each cup for $1.00 . This concept applies to any business, from small stands to large corporations, helping them determine the right price to ensure profitability.
To achieve a 33% gross profit margin on an item costing $56.78, the business needs to set the selling price at $84.75. This is calculated using the formula for gross profit margin. By rearranging the formula, we determined the necessary selling price to meet the desired profit margin.
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