SOLUTION: a three digit number is equal to17 times the sum of its digits. if 198 is added to the number, the digits are interchanged. the addition of first and third digit is 1less than

Algebra ->  Linear-equations -> SOLUTION: a three digit number is equal to17 times the sum of its digits. if 198 is added to the number, the digits are interchanged. the addition of first and third digit is 1less than       Log On


   

Question 1066226: a three digit number is equal to17 times the sum of its digits.
if 198 is added to the number, the digits are interchanged.
the addition of first and third digit is 1less than middle digit.
find the number
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Let h = the hundreds digit
Let t = the tens digit
Let u = the units (or ones) digit

a three digit number is equal to 17 times the sum of its digits. 
100h+10t+u = 17(h+t+u)
100h+10t+u = 17h+17t+17u
83h-7t-16u = 0

if 198 is added to the number, the digits are interchanged. 
100h+10t+u+198 = 100u+10t+h
       99h-99u = -198
           h-u = -2

the addition of first and third digit is 1 less than middle digit. 
  h+u = t-1
h-t+u = -1

find the number
Solve this system:

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

You finish.

Edwin