Question

The sum of three consecutive odd numbers is $153$. What is the number?

Answer 1

Find three consecutive odd numbers whose sum is $153$.

Let us assume that the first odd number is $\mathrm{x}$.

Then the second odd number is $\mathrm{x}+2$.

The third odd number is $\mathrm{x}+4$.

According to the question,

Sum of these three consecutive odd numbers $=153$

$\begin{array}{rcl}& \Rightarrow & \left(\mathrm{x}\right)+\left(\mathrm{x}+2\right)+\left(\mathrm{x}+4\right)=153\\ & \Rightarrow & 3\mathrm{x}+6=153\\ & \Rightarrow & 3\mathrm{x}=153-6\\ & \Rightarrow & 3\mathrm{x}=147\\ & \Rightarrow & \mathrm{x}=\frac{147}{3}\\ & \Rightarrow & \mathrm{x}=49\end{array}$

Thus, the first odd number $=\mathrm{x}=49$

Second odd number $=\mathrm{x}+2=49+2=51$

Third odd number $=\mathrm{x}+4=49+4=53$

Therefore the required numbers are $49,51,53$.