QuestionQuestion 3 (2 points) Frank owns a car dealership, and he is trying to understand how much more in margin(\ $) he makes from the average electric car compared to a regular car. Accordingly, he knows that his average cost of acquiring a regular car is$ \ $20,000$ , whereas his average cost of acquiring an electric vehicle is $\$ 28,000$ . He also knows that the markup(\%) on the regular car is $40 \%$ , whereas the margin(\%) of the electric vehicle is $30 \%$ . Based on this information, how much more in margin( $\$$ ) does Frank make when he sells an electric car compared to a regular car? $\$ 8000$ \ $12000 \$6000$ \ $4000$

Studdy Solution

STEP 1

1. The average cost of acquiring a regular car is $20,000.<br />2. The average cost of acquiring an electric vehicle is$ 28,000.
3. The markup percentage on the regular car is 40%.
4. The margin percentage of the electric vehicle is 30%.
5. We need to find the difference in margin (in dollars) between selling an electric car and a regular car.

STEP 2

1. Calculate the selling price of a regular car.
2. Calculate the margin in dollars for a regular car.
3. Calculate the selling price of an electric car.
4. Calculate the margin in dollars for an electric car.
5. Determine the difference in margin between the electric car and the regular car.

STEP 3

Calculate the selling price of a regular car using the markup percentage.
The selling price of a regular car is calculated as follows: $\text{Selling Price of Regular Car} = \text{Cost of Regular Car} + (\text{Markup Percentage} \times \text{Cost of Regular Car})$
$\text{Selling Price of Regular Car} = 20,000 + (0.40 \times 20,000)$ $\text{Selling Price of Regular Car} = 20,000 + 8,000$ $\text{Selling Price of Regular Car} = 28,000$

STEP 4

Calculate the margin in dollars for a regular car.
The margin for a regular car is the difference between the selling price and the cost: $\text{Margin for Regular Car} = \text{Selling Price of Regular Car} - \text{Cost of Regular Car}$
$\text{Margin for Regular Car} = 28,000 - 20,000$ $\text{Margin for Regular Car} = 8,000$

STEP 5

Calculate the selling price of an electric car using the margin percentage.
The selling price of an electric car is calculated as follows: $\text{Selling Price of Electric Car} = \frac{\text{Cost of Electric Car}}{1 - \text{Margin Percentage}}$
$\text{Selling Price of Electric Car} = \frac{28,000}{1 - 0.30}$ $\text{Selling Price of Electric Car} = \frac{28,000}{0.70}$ $\text{Selling Price of Electric Car} = 40,000$

STEP 6

Calculate the margin in dollars for an electric car.
The margin for an electric car is the difference between the selling price and the cost: $\text{Margin for Electric Car} = \text{Selling Price of Electric Car} - \text{Cost of Electric Car}$
$\text{Margin for Electric Car} = 40,000 - 28,000$ $\text{Margin for Electric Car} = 12,000$

STEP 7

Determine the difference in margin between the electric car and the regular car.
$\text{Difference in Margin} = \text{Margin for Electric Car} - \text{Margin for Regular Car}$ $\text{Difference in Margin} = 12,000 - 8,000$ $\text{Difference in Margin} = 4,000$
The difference in margin is:
$\boxed{4,000}$

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