A business purchases an item for $12.25. They want to make a gross profit margin of 45% on the item. What do they need to price the item at?
Selling Price = $[?]
Round to the nearest cent.
Answer (1)
Define the cost of the item C = $12.25 and the desired gross profit margin P = 45% = 0.45 .
Use the gross profit margin formula: P = S S − C , where S is the selling price.
Substitute the known values into the formula: 0.45 = S S − 12.25 .
Solve for S : S = 0.55 12.25 ≈ 22.27 . The selling price is 22.27 .
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.
Defining Variables Let's define some variables:
Cost of the item, C = $12.25
Gross profit margin, P = 45% = 0.45
Selling price, S = ? (what we want to find)
Stating the Formula The formula for gross profit margin is:
P = S S − C
Plugging in the Values Now, let's plug in the values we know:
0.45 = S S − 12.25
Solving for S Next, we solve for S :
0.45 S = S − 12.25
0.55 S = 12.25
S = 0.55 12.25
Calculating S Now, let's calculate the value of S :
S = 0.55 12.25 = 22.272727...
Rounding to the nearest cent, we get S = 22.27
Final Answer Therefore, the selling price needs to be $22.27 to achieve a 45% gross profit margin.
Examples
Imagine you're running a small bookstore. You buy a popular novel for $$10 and want to make a 60% profit margin to cover your costs and make a reasonable income. By using the gross profit margin formula, you can determine the optimal selling price for the novel. This ensures you're not only covering your initial investment but also achieving your desired profit, contributing to the financial health of your bookstore. This principle applies to various business scenarios, from pricing handmade crafts to setting service fees.
