Question 1066226
<pre>
Let h = the hundreds digit
Let t = the tens digit
Let u = the units (or ones) digit
</pre>
a three digit number is equal to 17 times the sum of its digits. 
<pre>
100h+10t+u = 17(h+t+u)
100h+10t+u = 17h+17t+17u
83h-7t-16u = 0
</pre>
if 198 is added to the number, the digits are interchanged. 
<pre>
100h+10t+u+198 = 100u+10t+h
       99h-99u = -198
           h-u = -2
</pre>
the addition of first and third digit is 1 less than middle digit. 
<pre>
  h+u = t-1
h-t+u = -1
</pre>
find the number
<pre>
Solve this system:

83h-7t-16u =  0
  h   -  u = -2
  h- t+  u = -1

You finish.

Edwin</pre>