Question

Three consecutive odd integers have a sum of
45. Find the integers.
would that be 5,7, and 9?

Answer 1

That would be incorrect, because 5+7+9=21 (not =45).

Answer 2

Let your middle integer be \(\color{black}{\displaystyle x }\) (this is the second consecutive even integer you are looking for).

Answer 3

Then, the smallest (the first) integer is \(\color{black}{\displaystyle x-2 }\) and the largest (the third) integer is \(\color{black}{\displaystyle x+2 }\).

Answer 4

You know that these have to add to 45, so we set:
\(\color{black}{\displaystyle (x-2)+x+(x+2)=45 }\)

where \(\color{black}{\displaystyle x }\) denotes the middle (the 2nd) of the consecutive odd integers.

Answer 5

Solve for \(x\), and from there you will know what the first odd integer and the third odd integer are.

Answer 6

Example:
Three consecutive odd integers have a sum of 39. Find the integers.

We can call the middle integer \(x\). (With this definition, \((x-2)\) and
\((x+2)\) are the first and third integers respectively.) Knowing that
the sum of these three is equal to 36, we set the following equation.

\(\color{black}{\displaystyle (x-2)+x+(x+2)=39}\)
\(\color{black}{\displaystyle 3x=39\quad\Longrightarrow\quad x=13.}\)

So, the middle number is \(13\), and therefore the remaining two are
\(11\) and \(15\). (There is the answer to the example: \(11\), \(13\), \(15\).)