a business purchases an item for $8.32. they want to make a gross profit margin of 57% on the item. what do…

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.

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 $x$

$x=\frac{8.32}{0.43}\approx19.35$.