The average of 4 consecutive even numbers is 27. What is the greatest number?

Options

A. 28
B. 26
C. 32
D. 30

Answer

To solve the problem of finding the greatest of 4 consecutive even numbers whose average is 27, we can follow these steps:

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

### Step 2: Express the four consecutive even numbers
The four consecutive even numbers can be expressed as:
- First number: \( n \)
- Second number: \( n + 2 \)
- Third number: \( n + 4 \)
- Fourth number: \( n + 6 \)

### Step 3: Set up the equation for the average
The average of these four numbers is given as 27. Therefore, we can set up the equation:
\[ \text{Average} = \frac{n + (n + 2) + (n + 4) + (n + 6)}{4} = 27 \]

### Step 4: Simplify the equation
Combine the terms in the numerator:
\[ \frac{4n + 12}{4} = 27 \]

### Step 5: Multiply both sides by 4
To eliminate the fraction, multiply both sides by 4:
\[ 4n + 12 = 108 \]

### Step 6: Solve for \( n \)
Subtract 12 from both sides:
\[ 4n = 108 - 12 \]
\[ 4n = 96 \]
Now, divide by 4:
\[ n = \frac{96}{4} = 24 \]

### Step 7: Find the four consecutive even numbers
Now that we have \( n = 24 \), we can find the four consecutive even numbers:
- First number: \( 24 \)
- Second number: \( 24 + 2 = 26 \)
- Third number: \( 24 + 4 = 28 \)
- Fourth number: \( 24 + 6 = 30 \)

### Step 8: Identify the greatest number
The greatest of these four consecutive even numbers is:
\[ 30 \]

Thus, the greatest number is **30**.

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