a business purchases an item for $6.50. they want to make a gross profit margin of 60% on the item. what do…

a business purchases an item for $6.50. they want to make a gross profit margin of 60% on the item. what do they need to price the item at? selling price = $?

a business purchases an item for $6.50. they want to make a gross profit margin of 60% on the item. what do they need to price the item at? selling price = $?

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 $x$. The cost price is $6.50$ and the gross - profit margin is $0.6$. So, $0.6=\frac{x - 6.50}{x}$.

Step2: Cross - multiply

Cross - multiplying gives $0.6x=x - 6.50$.

Step3: Rearrange the equation

Subtract $0.6x$ from both sides: $0=x - 0.6x-6.50$. Then simplify to get $0 = 0.4x-6.50$.

Step4: Solve for $x$

Add $6.50$ to both sides: $6.50 = 0.4x$. Then divide both sides by $0.4$: $x=\frac{6.50}{0.4}=16.25$.

Answer:

$16.25$