Question 252616
This is how I would tackle the problem:

The three digit number can be represent as {{{100x+10y+z}}} where 100x is the hundreds, 10y is the tens and z is the units.

We know that {{{100x+10y+z = 43(x+y+z)}}}. We know that the three digit number is divisible by 5 which means that z must be either 0 or 5.

We know that x-2 = y.

Lets assume that z = 0. Collect terms in the equation {{{100x+10y+z = 43(x+y+z)}}}

{{{100x+10y = 43x+43y}}}
{{{57x-33y = 0}}}

Substitute x-2 in for y to give {{{57x-33(x-2) = 0}}}

{{{57x-33x+66 = 0}}}
{{{24x+66 = 0}}}
{{{x= -66/24}}}

x must be an integer, so we know z must be 5.

Collect terms in the equation {{{100x+10y+z = 43(x+y+z)}}}
{{{100x+10y+5 = 43x+43y+215}}}
{{{57x-33y-210= 0}}}

Substitute x-2 in for y to give {{{57x-33(x-2)-210 = 0}}}
{{{57x-(33x-66)-210 = 0}}}
{{{24x+66-210 = 0}}}
{{{24x = 144}}}
{{{x = 6}}}

S0 we know that the 3 digit number is 645.