Question

The sum of three consecutive odd integers is $ 231, $ how do you find the integers?

Answer 1

Hint: Here we will set up an equation based on the given word statements. Here we will assume the first odd integer to be “x” and since every consecutive odd integer are separated by the difference of count “2” so will assume accordingly and place the sum of values for it.

Complete step by step solution:
Let us assume the first integer is “x” ….. (A)
The second consecutive odd integer be ….. (B)
And the third consecutive odd integer be ….. (C)
Given that the sum of the three consecutive odd integers is $ 231 $
So, the equation becomes-
 $ x + (x + 2) + (x + 4) = 231 $
Simplify the above equations by pairing the like terms together.
 $ \Rightarrow \underline {x + x + x} + \underline {2 + 4} = 231 $
Add the like terms-
 $ \Rightarrow 3x + 6 = 231 $
Move all like terms on one side of the equation. When you move any term from one side of the equation to the opposite side, then the sign of the terms also changes. Positive term become negative and the negative term becomes positive.
 $ \Rightarrow 3x = 231 - 6 $
Simplify the above equation finding the difference on the right hand side of the equation-
 $ \Rightarrow 3x = 225 $
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
 $ \Rightarrow x = \dfrac{{225}}{3} $
Find factors for the term on the numerator.
 $ \Rightarrow x = \dfrac{{3 \times 75}}{3} $
Common factors from the numerator and the denominator cancel each other.
 $ \Rightarrow x = 75 $
By using equations (A), (B) and (C)
Therefore, the three consecutive numbers are $ 75,{\text{ 77, 79}} $
So, the correct answer is “ $ 75,{\text{ 77, 79}} $ ”.

Note: Be careful about the sign convention. When you move any term from one side of the equation to the opposite side then the sign of the term also changes. Positive terms become negative and the negative term becomes positive.