Question

The sum of 3 consecutive numbers is 33. Find those numbers.

Answer 1

Hint: To find the three consecutive numbers, we will assume these as x, $x+1$ and $x+2$ . Then, according to the given condition, we can form an equation. We have to solve this equation and find the value of x. Then, we have to substitute the value of x in the assumed consecutive numbers.

Complete step by step answer:
We are given that the sum of 3 consecutive numbers is 33. Let us consider one number to be x. We know that consecutive numbers are the numbers that follow each other continuously in the order from smallest to largest. Let us consider the next two consecutive numbers as $x+1$ and $x+2$ . Therefore, according to the given condition, we can form an equation as shown below.
$\begin{align}
  & \Rightarrow x+\left( x+1 \right)+\left( x+2 \right)=33 \\
 & \Rightarrow x+x+1+x+2=33 \\
\end{align}$
We have to solve for x. First, let us add the like terms.
$\Rightarrow 3x+3=33$
Let us take the common factor 3 from the LHS.
$\Rightarrow 3\left( x+1 \right)=33$
We have to take 3 from the LHS to the RHS.
$\begin{align}
  & \Rightarrow x+1=\dfrac{33}{3} \\
 & \Rightarrow x+1=11 \\
\end{align}$
Let us collect constants on one side.
$\begin{align}
  & \Rightarrow x=11-1 \\
 & \Rightarrow x=10 \\
\end{align}$
Therefore, one number will be 10. To find the next number, that is $x+1$ , we have to substitute the value of x here.
$\Rightarrow x+1=10+1=11$
Let us find the next consecutive number.
$\Rightarrow x+2=10+2=12$

Hence, the three consecutive numbers are 10, 11, 12.

Note: Students must thoroughly understand the concept of algebraic equations, the rules and properties associated with it and the methods to solve these equations. We can also solve this question in an alternate way. We can also consider the consecutive numbers as $x-1$ , x and $x+1$ . Then, according to the given condition, we can write
$\begin{align}
  & \Rightarrow \left( x-1 \right)+x+\left( x+1 \right)=33 \\
 & \Rightarrow 3x=33 \\
 & \Rightarrow x=\dfrac{33}{3} \\
 & \Rightarrow x=11 \\
\end{align}$
Therefore, one number is 11. Let us substitute this value of x in $x-1$ .
$\Rightarrow x-1=11-1=10$
The other number can be found by substituting the value of x in $x+1$ .
$\Rightarrow x+1=11+1=12$
Therefore, the 3 consecutive numbers are 10, 11, 12.