Summation of 5 consecutive numbers is found out to be 335. If we add the largest and smallest number what will we get?

Options

A. a. 134
B. b. 150
C. c. 174
D. d. 226

Answer

To solve the problem step by step, we will first define the five consecutive numbers and then find their sum. Finally, we will calculate the sum of the largest and smallest numbers.

### Step 1: Define the smallest number
Let the smallest of the five consecutive numbers be \( x \).

### Step 2: Write the five consecutive numbers
The five consecutive numbers can be expressed as:
- Smallest: \( x \)
- Second smallest: \( x + 1 \)
- Middle: \( x + 2 \)
- Second largest: \( x + 3 \)
- Largest: \( x + 4 \)

### Step 3: Write the equation for their sum
The sum of these five consecutive numbers is given by:
\[ x + (x + 1) + (x + 2) + (x + 3) + (x + 4) \]
This simplifies to:
\[ 5x + (1 + 2 + 3 + 4) = 5x + 10 \]

### Step 4: Set up the equation
According to the problem, the sum of these numbers is 335:
\[ 5x + 10 = 335 \]

### Step 5: Solve for \( x \)
To find \( x \), we first subtract 10 from both sides:
\[ 5x = 335 - 10 \]
\[ 5x = 325 \]
Now, divide both sides by 5:
\[ x = \frac{325}{5} = 65 \]

### Step 6: Identify the largest and smallest numbers
Now that we have \( x \), we can find the smallest and largest numbers:
- Smallest number: \( x = 65 \)
- Largest number: \( x + 4 = 65 + 4 = 69 \)

### Step 7: Calculate the sum of the largest and smallest numbers
Now, we need to find the sum of the largest and smallest numbers:
\[ 65 + 69 = 134 \]

### Final Answer
The sum of the largest and smallest numbers is \( 134 \).

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