Question

When the smallest of three consecutive odd integers is added to four times the larges, it produces a result $729$ more than four times the middle integer. Find the numbers.

Answer 1

Let the three integers be $x$, $x+2$ and $x+4$
Now from the given information, the equation we get is
$x+4(x+4)=4(x+2)+729$
$\Rightarrow x+4x+16=4x+8+729$
$\Rightarrow 5x-4x=737-16$
$\Rightarrow x=721$
So the three consecutive odd integers are,
$x=721$
$x+2=723$,
and $x+4=725$

Therefore, the numbers are $721,723,725$.