Four consecutive even numbers are such that 3 times of the first number is equal to twice the third number. The sum of all the four numbers is :

Options

A. 20
B. 40
C. 44
D. can't be determined

Answer

To solve the problem step by step, let's define the four consecutive even numbers and set up the equation based on the information provided.

### Step 1: Define the first even number
Let the first even number be \( x \).

### Step 2: Define the consecutive even numbers
Since we are looking for four consecutive even numbers, we can express them as:
- First number: \( x \)
- Second number: \( x + 2 \)
- Third number: \( x + 4 \)
- Fourth number: \( x + 6 \)

### Step 3: Set up the equation
According to the problem, 3 times the first number is equal to twice the third number. We can write this as:
\[ 3x = 2(x + 4) \]

### Step 4: Solve the equation
Now, let's solve the equation:
1. Distribute the right side:
\[ 3x = 2x + 8 \]
2. Subtract \( 2x \) from both sides:
\[ 3x - 2x = 8 \]
\[ x = 8 \]

### Step 5: Find the four consecutive even numbers
Now that we have \( x = 8 \), we can find the four consecutive even numbers:
- First number: \( 8 \)
- Second number: \( 8 + 2 = 10 \)
- Third number: \( 8 + 4 = 12 \)
- Fourth number: \( 8 + 6 = 14 \)

### Step 6: Calculate the sum of the four numbers
Now, we can find the sum of these four numbers:
\[ 8 + 10 + 12 + 14 \]
Calculating this gives:
\[ 8 + 10 = 18 \]
\[ 18 + 12 = 30 \]
\[ 30 + 14 = 44 \]

### Final Answer
The sum of all four numbers is \( 44 \).

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