a business purchases an item for $4.53. they want to make a gross profit margin of 82% on the item. what do…

a business purchases an item for $4.53. they want to make a gross profit margin of 82% 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 $4.53. they want to make a gross profit margin of 82% 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

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 $C = 4.53$, and the gross - profit margin $G = 0.82$. So, $0.82=\frac{x - 4.53}{x}$.

Step2: Cross - multiply

Cross - multiplying gives $0.82x=x - 4.53$.

Step3: Rearrange the equation

Subtract $0.82x$ from both sides: $0=x - 0.82x-4.53$. Then simplify the left - hand side: $0 = 0.18x-4.53$.

Step4: Solve for $x$

Add $4.53$ to both sides: $4.53 = 0.18x$. Then divide both sides by $0.18$: $x=\frac{4.53}{0.18}\approx25.17$.

Answer:

$25.17$