a business purchases an item for $32.32. they want to make a gross profit margin of 27% on the item. what do…

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.

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

Explanation:

Step1: Recall the gross - profit - margin formula

The gross - profit - margin formula is $\text{Gross Profit Margin}=\frac{\text{Selling Price}-\text{Cost Price}}{\text{Selling Price}}$. Let the selling price be $x$ and the cost price $C = 32.32$, and the gross - profit margin $G=0.27$. So, $0.27=\frac{x - 32.32}{x}$.

Step2: Cross - multiply

Cross - multiplying gives $0.27x=x - 32.32$.

Step3: Rearrange the equation

Move the terms with $x$ to one side: $32.32=x - 0.27x$.

Step4: Combine like terms

$32.32 = 0.73x$.

Step5: Solve for $x$

$x=\frac{32.32}{0.73}$. $x = 44.273973$.

Step6: Round to the nearest cent

Rounding $44.273973$ to the nearest cent gives $44.27$.

Answer:

$44.27$