The sum of seven consecutive numbers is 168. What is the sum of the first and the last number?

Options

A. 58
B. 49
C. 48
D. 47

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the first number
Let the first of the seven consecutive numbers be represented as \( x \).

### Step 2: Write the consecutive numbers
The seven consecutive numbers can be expressed as:
- First number: \( x \)
- Second number: \( x + 1 \)
- Third number: \( x + 2 \)
- Fourth number: \( x + 3 \)
- Fifth number: \( x + 4 \)
- Sixth number: \( x + 5 \)
- Seventh number: \( x + 6 \)

### Step 3: Set up the equation for the sum
The sum of these seven consecutive numbers is given as 168. Therefore, we can write the equation:
\[ x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6) = 168 \]

### Step 4: Simplify the equation
Combine like terms:
\[ 7x + (1 + 2 + 3 + 4 + 5 + 6) = 168 \]
Calculating the sum of the numbers from 1 to 6:
\[ 1 + 2 + 3 + 4 + 5 + 6 = 21 \]
So, the equation becomes:
\[ 7x + 21 = 168 \]

### Step 5: Solve for \( x \)
Subtract 21 from both sides:
\[ 7x = 168 - 21 \]
\[ 7x = 147 \]
Now, divide by 7:
\[ x = \frac{147}{7} = 21 \]

### Step 6: Find the first and last numbers
The first number is \( x = 21 \) and the last number is:
\[ x + 6 = 21 + 6 = 27 \]

### Step 7: Calculate the sum of the first and last numbers
Now, we need to find the sum of the first and last numbers:
\[ 21 + 27 = 48 \]

### Final Answer
The sum of the first and last number is \( 48 \).

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