Let's solve the problem step by step.
First, we need to understand what a margin is in this context. The margin is the percentage of the final selling price that is profit.
The cost of the item is given as [tex]$20.00, and the margin is 20%. This means that the margin is 20% of the retail price, not the cost price.
Let's denote the retail price as \( R \).
The margin is calculated by taking the retail price and subtracting the cost of the item:
\[ \text{Margin} = R - \text{Cost} \]
Since the margin is 20% of the retail price, we can also write it as:
\[ \text{Margin} = 0.20 \times R \]
Thus, our equation expressing the margin in two ways becomes:
\[ 0.20 \times R = R - 20.00 \]
Now we want to solve for \( R \). To do this, we can collect all terms involving \( R \) on one side of the equation:
\[ 0.20R + 20.00 = R \]
Subtracting \( 0.20R \) from both sides of the equation, we get:
\[ 20.00 = R - 0.20R \]
\[ 20.00 = 0.80R \]
To isolate \( R \), we divide both sides by 0.80:
\[ 20.00 \div 0.80 = R \]
\[ R = 25.00 \]
Therefore, the retail price will be $[/tex]25.00.
The provided options do not include $25.00, so it seems there might have been a mistake in the options given. If we are constrained to choose from the provided options, none of them is the correct answer.
