A used-car lot has 4-door sedans, 2-door sedans, sports cars, vans, and jeeps. Of these vehicles, 40% are 4-door sedans, 25% are 2-door sedans, 20% are sports cars, 10% are vans, and 10 of the vehicles are jeeps. If this car lot has no other vehicles, how many vehicles are on the used-car lot?

Options

A. `300`
B. `400`
C. `480`
D. `600`

Answer

To find the total number of vehicles on the used-car lot, we can follow these steps:

### Step 1: Define the total number of vehicles
Let \( x \) be the total number of vehicles on the used-car lot.

### Step 2: Calculate the number of each type of vehicle
- **4-door sedans**: 40% of \( x \)
\[ \text{Number of 4-door sedans} = 0.4x \]

- **2-door sedans**: 25% of \( x \)
\[ \text{Number of 2-door sedans} = 0.25x \]

- **Sports cars**: 20% of \( x \)
\[ \text{Number of sports cars} = 0.2x \]

- **Vans**: 10% of \( x \)
\[ \text{Number of vans} = 0.1x \]

### Step 3: Calculate the total percentage of vehicles accounted for
Now, we can sum up the percentages of the vehicles we have calculated:
\[ \text{Total percentage of known vehicles} = 0.4x + 0.25x + 0.2x + 0.1x \]

### Step 4: Simplify the equation
Combine the terms:
\[ 0.4x + 0.25x + 0.2x + 0.1x = 0.95x \]

### Step 5: Determine the number of jeeps
Since the total number of vehicles is \( x \), the number of jeeps can be calculated as:
\[ \text{Number of jeeps} = x - 0.95x = 0.05x \]

### Step 6: Set up the equation using the number of jeeps
According to the problem, there are 10 jeeps. Thus, we have:
\[ 0.05x = 10 \]

### Step 7: Solve for \( x \)
To find \( x \), divide both sides by 0.05:
\[ x = \frac{10}{0.05} = 200 \]

### Conclusion
The total number of vehicles on the used-car lot is \( \boxed{200} \).

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