Four consecutive even numbers are such that 3 times of the first number is equal to twice of the third of the 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 denote the first even number as \( a \). The four consecutive even numbers can then be expressed as follows:

1. First even number: \( a \)
2. Second even number: \( a + 2 \)
3. Third even number: \( a + 4 \)
4. Fourth even number: \( a + 6 \)

According to the problem, we know that 3 times the first number is equal to twice the third number. We can write this relationship as an equation:

\[ 3a = 2(a + 4) \]

Now, let's solve this equation step by step.

### Step 1: Expand the equation
We expand the right side of the equation:

\[ 3a = 2a + 8 \]

### Step 2: Rearrange the equation
Next, we will rearrange the equation to isolate \( a \):

\[ 3a - 2a = 8 \]

### Step 3: Simplify the equation
Now, simplify the left side:

\[ a = 8 \]

### Step 4: Determine the four consecutive even numbers
Now that we have \( a \), we can find the four consecutive even numbers:

1. First even number: \( a = 8 \)
2. Second even number: \( a + 2 = 10 \)
3. Third even number: \( a + 4 = 12 \)
4. Fourth even number: \( a + 6 = 14 \)

### Step 5: Calculate the sum of the four numbers
Now, we can find the sum of these four consecutive even numbers:

\[ 8 + 10 + 12 + 14 \]

Calculating this gives:

\[ 8 + 10 = 18 \]
\[ 18 + 12 = 30 \]
\[ 30 + 14 = 44 \]

Thus, the sum of all four numbers is \( 44 \).

### Final Answer
The sum of all the four consecutive even numbers is \( \boxed{44} \).

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