a business purchases an item for $7.36. they ...
a business purchases an item for $7.36. they want to make a gross profit margin of 30% on the item. what do they need to price the item at? selling price = $?
Answer
# Answer:
$10.51$
# Explanation:
## Step1: Recall 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 $7.36$ and the gross - profit margin is $0.3$. So, $0.3=\frac{x - 7.36}{x}$.
## Step2: Cross - multiply
Cross - multiplying gives $0.3x=x - 7.36$.
## Step3: Rearrange the equation
Subtract $0.3x$ from both sides: $0=x - 0.3x-7.36$. Then, $0 = 0.7x-7.36$.
## Step4: Solve for $x$
Add $7.36$ to both sides: $7.36 = 0.7x$. Then, $x=\frac{7.36}{0.7}\approx10.51$.