a business purchases an item for $352.62. they want to make a gross profit margin of 24% on the item. what…

a business purchases an item for $352.62. they want to make a gross profit margin of 24% on the item. what do they need to price the item at? selling price = $?

a business purchases an item for $352.62. they want to make a gross profit margin of 24% on the item. what do they need to price the item at? selling price = $?

Answer

Answer:

$464$

Explanation:

Step1: Define cost and margin

Let cost $C = 352.62$, margin $m=0.24$.

Step2: Use margin formula

The formula for gross - profit margin is $m=\frac{S - C}{S}$, where $S$ is the selling price. Rearranging gives $mS=S - C$, then $C = S(1 - m)$.

Step3: Solve for selling price

$S=\frac{C}{1 - m}=\frac{352.62}{1 - 0.24}=\frac{352.62}{0.76}=464$.