Three consecutive integers odd up to 258. What is the smallest integer?

Options

A. `58`
B. `85`
C. `86`
D. `89`

Answer

To solve the problem of finding the smallest of three consecutive integers that add up to 258, we can follow these steps:

### Step 1: Define the integers
Let the first integer be \( x \). Since we are looking for three consecutive integers, the second integer will be \( x + 1 \) and the third integer will be \( x + 2 \).

### Step 2: Set up the equation
The sum of these three consecutive integers can be expressed as:
\[ x + (x + 1) + (x + 2) = 258 \]

### Step 3: Simplify the equation
Combine the terms on the left side:
\[ x + x + 1 + x + 2 = 258 \]
This simplifies to:
\[ 3x + 3 = 258 \]

### Step 4: Solve for \( x \)
Subtract 3 from both sides of the equation:
\[ 3x = 258 - 3 \]
\[ 3x = 255 \]
Now, divide both sides by 3:
\[ x = \frac{255}{3} \]
\[ x = 85 \]

### Step 5: Identify the smallest integer
The smallest integer is \( x \), which we found to be 85.

### Final Answer
The smallest integer is **85**.