Question 456236
Let x= the hundreds digit
and let y=the tens digit
and z=the units digit
Now we are told that x+y+z=15----eq1
We know that the original number is: 
100x+10y+z
If the tens and units digits are interchanged, the new number will be:
100x+10z+y

Now we are also told that:
100x+10y+z=100x+10z+y+9 simplify by subtracting 100x+10z+y from each side
100x-100x+10y-y+z-10z=9 collect like terms
9y-9z=9 or
y-z=1-------------------------------eq2

If the units and hundreds digits are interchanged, we have:
100z+10y+x and this number is 99 more than the original number, so:

100z+10y+x=100x+10y+z+99 simplify by subtracting 100x+10y+z from each side
100z-z+10y-10y+x-100x=99
99z-99x=99 or
z-x=1------------------------------eq3
From eq2, y=1+z and from eq3, x=z-1
substitute these values into eq1 for  for x and y and we get:
z-1+z+1+z=15
3z=15
z=5
Now from eq2:
y-5=1
y=6
and from eq3
x=5-1=4
So the original number is:
465------------------------------ans

CK
465 is 9 more than 456, and
564 is 99 more than 465

Hop this helps---ptaylor