a business purchases an item for $109.78. they want to make a gross profit margin of 12% on the item. what…

a business purchases an item for $109.78. they want to make a gross profit margin of 12% 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 $109.78. they want to make a gross profit margin of 12% on the item. what do they need to price the item at? selling price = $? round to the nearest cent.

Answer

Explanation:

Step1: Define the cost - price and profit - margin

The cost price (CP) of the item is $CP = 109.78$, and the gross - profit margin is $12%=0.12$. The formula for the gross - profit margin is $\text{Gross Profit Margin}=\frac{\text{Selling Price}-\text{Cost Price}}{\text{Selling Price}}$. Let the selling price be $SP$. So, $0.12=\frac{SP - 109.78}{SP}$.

Step2: Cross - multiply the equation

Cross - multiplying gives $0.12SP=SP - 109.78$.

Step3: Rearrange the equation

Move the terms with $SP$ to one side: $109.78 = SP-0.12SP$.

Step4: Combine like terms

$109.78=(1 - 0.12)SP=0.88SP$.

Step5: Solve for $SP$

$SP=\frac{109.78}{0.88}$. $SP = 124.75$.

Answer:

$124.75$