Question

The sum of $3$ consecutive odd numbers is $27$, how do you find the numbers?

Answer 1

Step 1:Solve the integers

Let the smallest odd integer of the three be $\mathrm{x}$

Hence the next $2$consecutive odd integers are $\mathrm{x}+2$and $\mathrm{x}+4$.

Since the sum of the three integers is $27$, we may write

$(\mathrm{x})+(\mathrm{x}+2)+(\mathrm{x}+4)=27$

$\Rightarrow \mathrm{x}+\mathrm{x}+2+\mathrm{x}+4=27$

$\Rightarrow 3\mathrm{x}+6=27$

Step 2:Find the numbers

Subtracting $6$ on both sides

$\Rightarrow 3\mathrm{x}+6-6=27-6$

$\Rightarrow 3\mathrm{x}=21$

$\Rightarrow \mathrm{x}=\frac{21}{3}$

$\Rightarrow \mathrm{x}=7$

So, First number$=\mathrm{x}=7$
Second number$=\mathrm{x}+2=7+2=9$
Third number $=\mathrm{x}+4=7+4=11$

Hence, the three required integers are $7,9,11$.