a business purchases an item for $66.75. they want to make a gross profit margin of 20% on the item. what do…

a business purchases an item for $66.75. they want to make a gross profit margin of 20% 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 $66.75. they want to make a gross profit margin of 20% on the item. what do they need to price the item at? selling price = $? round to the nearest cent.

Answer

Answer:

$83.44

Explanation:

Step1: Define cost and margin

Let cost $C = 66.75$, margin $m=0.2$.

Step2: Use margin formula

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

Step3: Calculate selling price

Substitute $C = 66.75$ and $m = 0.2$ into the formula: $S=\frac{66.75}{1 - 0.2}=\frac{66.75}{0.8}=83.4375$.

Step4: Round the result

Rounding $83.4375$ to the nearest cent gives $83.44$.