Question

Solve the following problems:

The sum of three consecutive odd numbers is $147$. Find the numbers.

Answer 1

Given, the sum of three consecutive odd numbers is $147$.

Let the four consecutive numbers be $\mathrm{x},\mathrm{x}+2,\mathrm{x}+4$

According to the given condition,

$$\begin{gathered} \Rightarrow \mathrm{x}+(\mathrm{x}+2)+(\mathrm{x}+4)=147 \\ \Rightarrow \mathrm{x}+\mathrm{x}+2+\mathrm{x}+4=147 \\ \Rightarrow 3\mathrm{x}+6=147 \\ \Rightarrow 3\mathrm{x}+6-6=147-6[\mathrm{Subtracting}6\mathrm{from}\mathrm{both}\mathrm{sides}] \\ \Rightarrow 3\mathrm{x}=141 \\ \Rightarrow \frac{3\mathrm{x}}{3}=\frac{141}{3}[\mathrm{Dividing}\mathrm{both}\mathrm{sides}\mathrm{by}3] \\ \therefore \mathrm{x}=47 \end{gathered}$$

Therefore, four consecutive numbers are $47,47+2=49,47+4=51$

Hence, $47,49\mathrm{and}51$are the required three consecutive odd numbers.