In a line of 50 vehicles, a blue sedan is 15th from the front and a red SUV is 18th from the rear. How many vehicles are parked between the blue sedan and the red SUV?

The correct answer is 17.

Step-by-Step Explanation:

1. Identify the Given Information:

Total number of vehicles in the line = 50

Position of the blue sedan from the front = 15th

Position of the red SUV from the rear = 18th

2. Method 1: Direct Subtraction from Total Vehicles

Since the blue sedan is counted from the front and the red SUV is counted from the rear, we can find the number of vehicles between them by subtracting the sum of their positions from the total number of vehicles:

$\text{Vehicles between}=\text{Total vehicles}-(\text{Position from front}+\text{Position from rear})$

Substitute the given values into the formula:

$\text{Vehicles between}=50-(15+18)$

$\text{Vehicles between}=50-33=17$

3. Method 2: Finding Position from the Front

Alternatively, we can find the position of the red SUV from the front using the formula:

Position from front = Total vehicles - Position from rear + 1

$\text{Red SUV position from front}=50-18+1=33$

Now, the blue sedan is at position 15 and the red SUV is at position 33 from the front. The number of vehicles parked between position 15 and position 33 is:

$\text{Vehicles between}=33-15-1=17$

Therefore, there are 17 vehicles parked between the blue sedan and the red SUV.