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Three consecutive integers odd up to 258...

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

A

`58`

B

`85`

C

`86`

D

`89`

Text Solution

AI Generated Solution

The correct Answer is:
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**.
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