Question

The sum of three consecutive odd numbers is 27, how do you find the number?

Answer 1

Hint: We first recall the definition of consecutive integers. We know that the odd number occurs at the difference of two. We assume the first odd integer as $x$ then the next consecutive odd integer will be $x+2$ and then the third consecutive odd integer is $x+4$ . We add them and equate to $27$ . We solve for $x$ and then find the value of (x+ 2) and (x + 4).

Complete step by step answer:
We know that consecutive numbers are numbers which follow each other in order, without gaps, from smallest to largest. The consecutive odd integers are integers that follow each other by a difference of 2 and all the numbers must be odd.
So, let us assume the first consecutive odd integer as $x$, then the second consecutive odd integer that follow $x$ will be incremented by 2 as $x+2$ and the third consecutive integer will follow $x+2$ and will be incremented by 2 as $x+2+2=x+4$ .
We are given the question that the sum of three consecutive integers is 27. So, we add the consecutive odd integers in terms of $x$ and equate the sum to 27 . then we will get:
$\begin{align}
  & \Rightarrow \left( x \right)+\left( x+2 \right)+\left( x+4 \right)=27 \\
 & \Rightarrow x+x+x+2+4=27 \\
 & \\
\end{align}$
We add the variable terms and constant terms in the left-hand side of the above equation to have-
$\Rightarrow 3x+6=27$
We take 3 common in the left-hand side to have;
$\Rightarrow 3\left( x+2 \right)=27$
We divide both sides of above equation by 3 to have;
$\begin{align}
  & \Rightarrow \dfrac{3\left( x+2 \right)}{3}=\dfrac{27}{3} \\
 & \Rightarrow \left( x+2 \right)=9 \\
\end{align}$
We subtract both sides of above equation by 2 to have;
$\Rightarrow x+2-2=9-2=7$
$\therefore x=7$
So, the three consecutive odd integers are:
$\begin{align}
  & \Rightarrow x=7 \\
 & \Rightarrow x+2=7+2=9 \\
 & \Rightarrow x+4=7+4=11 \\
\end{align}$
We can see the obtained integers are odd and they are at a difference of 2 and when we add them we are getting 27. So, our answer is also verified.
This is our required solution.

Note:
We can verify our results by adding the three consecutive odd integers as $\Rightarrow 7+9+11=27$ . We note that when we add, subtract, multiply the same number or divide the same non-zero number both sides then the equation remains balanced which means the equality holds. If there are variable terms on both sides of the equation we should try to bring variable term at one side and constant term at other side.