Question

If the sum of three consecutive natural numbers starting from $x$ is $21,$ find the simplified algebraic expression for the sum and also find all the three numbers.

• A. Simplified expression for sum $=3x+3$
  Three consecutive natural numbers $=6,7$ and $8$
• B. Simplified expression for sum $=3x+2$
  Three consecutive natural numbers $=7,8$ and $9$
• C. Simplified expression for sum $=3x+1$
  Three consecutive natural numbers $=9,10$ and $11$
• D. Simplified expression for sum $=3x+3$
  Three consecutive natural numbers $=8,9$ and $10$

Answer 1

The correct option is A Simplified expression for sum $=3x+3$

Three consecutive natural numbers $=6,7$ and $8$
$\underset{–}{\text{Given:}}$
Smallest of the three numbers $=x$
So, three consecutive natural numbers would be:
$x,x+1,x+2$

The sum of these $3$ natural numbers is given as $21$, i.e.,
$\left(x\right)+(x+1)+(x+2)=21$

Combining the like terms together:

$\Rightarrow \underset{–}{(x+x+x)}+\underset{–}{(1+2)}=21$

$\Rightarrow 3x+3=21$

$3x+3$ is the simplified expression representing the sum of three consecutive numbers, where $x$ is any natural number.

Subtracting $3$ from both the sides of the above equation:
$\Rightarrow 3x+3-3=21-3$

$\Rightarrow 3x+\underset{–}{3-3}=\underset{–}{21-3}$

$\Rightarrow 3x+0=18$

$\Rightarrow 3x=18$
Dividing both sides of the equation by $3$:

$\Rightarrow \frac{3x}{3}=\frac{18}{3}$

$\Rightarrow x=6$

The smallest among three consecutive natural numbers is $6$. And other natural numbers are:
$x+1=6+1=7$ and
$x+2=6+2=8$

As a result, three consecutive natural numbers whose sum is $21$ are $6,7$ and $8$.

Therefore, option (a.) is the correct answer.