There are 20 vehicles-cars and motor cycles in a parking area. If there are 56 wheels together, how many cars are there?

Options

A. 8
B. 10
C. 12
D. 20

Answer

To solve the problem, we need to find out how many cars are in the parking area given the total number of vehicles and wheels. Let's break it down step by step.

### Step 1: Define Variables
Let:
- \( x \) = number of cars
- \( y \) = number of motorcycles

### Step 2: Set Up Equations
From the problem, we know:
1. The total number of vehicles (cars and motorcycles) is 20:
\[ x + y = 20 \quad \text{(Equation 1)} \]

2. The total number of wheels is 56. Since cars have 4 wheels and motorcycles have 2 wheels, we can express this as:
\[ 4x + 2y = 56 \quad \text{(Equation 2)} \]

### Step 3: Solve Equation 1 for one variable
From Equation 1, we can express \( y \) in terms of \( x \):
\[ y = 20 - x \]

### Step 4: Substitute into Equation 2
Now, substitute \( y \) in Equation 2:
\[ 4x + 2(20 - x) = 56 \]
Expanding this gives:
\[ 4x + 40 - 2x = 56 \]

### Step 5: Simplify the Equation
Combine like terms:
\[ 2x + 40 = 56 \]

### Step 6: Isolate \( x \)
Subtract 40 from both sides:
\[ 2x = 56 - 40 \]
\[ 2x = 16 \]

### Step 7: Solve for \( x \)
Divide both sides by 2:
\[ x = \frac{16}{2} = 8 \]

### Step 8: Conclusion
Thus, the number of cars \( x \) is 8.