a business purchases an item for $8.32. they ...
a business purchases an item for $8.32. they want to make a gross profit margin of 57% on the item. what do they need to price the item at? selling price = $? round to the nearest cent.
Answer
# Answer:
$19.35$
# Explanation:
## Step1: Recall gross - profit - margin formula
Gross profit margin $=\frac{\text{Selling Price}-\text{Cost Price}}{\text{Selling Price}}$
Let the selling price be $x$. The cost price is $8.32$ and the gross - profit margin is $0.57$. So, $0.57=\frac{x - 8.32}{x}$.
## Step2: Cross - multiply
$0.57x=x - 8.32$.
## Step3: Rearrange the equation
$x-0.57x = 8.32$.
## Step4: Simplify the left - hand side
$0.43x=8.32$.
## Step5: Solve for $x$
$x=\frac{8.32}{0.43}\approx19.35$.