Question

Find three consecutive odd integers whose sum is 171.

Short answer

The integers are $55,57,59$.

Step-by-step solution

Step 1. Given information 

We have been given that the sum of three consecutive odd integers is 171.

We have to find the integers.

Step 2. Form the equation 

Let the first odd integer is x.

So, the next two consecutive odd integers will be $x+2,x+4$.

As per the given statement,

We have,

$x+(x+2)+(x+4)=171$

Step 3. Solve the equation 

Solve for the value of x,

$$\begin{gathered} x+(x+2)+(x+4)=171 \\ 3x+6=171 \\ 3x=165 \\ x=55 \end{gathered}$$

The second odd integer will be :

$$\begin{gathered} x+2 \\ =55+2 \\ =57 \end{gathered}$$

Similarly the third odd integer will be :$59$