Question

Find three consecutive odd integers whose sum is 291.

Short answer

The integers are $95,97,99$.

Step-by-step solution

Step 1. Given information 

We have been given that the sum of three consecutive odd integers is 291.

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,

$x+x+2+x+4=291$

Step 3. Solve the equation 

$$\begin{gathered} x+x+2+x+4=291 \\ 3x+6=291 \\ 3x=291-6 \\ 3x=285 \\ x=\frac{285}{3} \\ x=95 \end{gathered}$$

Thus $x+2=97$and $x+4=99$.