a business purchases an item for $100. they want to make a gross profit margin of 70% on the item. what do…

a business purchases an item for $100. they want to make a gross profit margin of 70% 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 $100. they want to make a gross profit margin of 70% on the item. what do they need to price the item at? selling price = $? round to the nearest cent.

Answer

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 $100$ and the gross - profit margin is $0.7$. So, $0.7=\frac{x - 100}{x}$.

Step2: Cross - multiply

$0.7x=x - 100$.

Step3: Rearrange the equation

$100=x - 0.7x$.

Step4: Simplify the right - hand side

$100 = 0.3x$.

Step5: Solve for $x$

$x=\frac{100}{0.3}\approx333.33$.

Answer:

$333.33$