Question

Find three consecutive odd numbers whose sum is $219$.

Answer 1

Step 1: Calculate one of the numbers

Let us assume the three consecutive even numbers as $x,x+2$ and $x+4$.

It is given that the sum of these three numbers is $219$.

$\therefore x+x+2+x+4=219$

$\Rightarrow$ $3x+6=219$

$\Rightarrow$ $3x=219-6$

$\Rightarrow$ $x=\frac{213}{3}$

$\Rightarrow$ $x=71$

Step 2: Calculate the other two numbers

Therefore,

$x+2=71+2=73$

$x+4=71+4=75$

Hence, the three consecutive odd numbers are $71,73$ and $75$.