SOLUTION: the sum of the digits of a number of three digits is 18. if the number is divided by the sum of the ten's and hundred digits the qoutient is 38 the remainder is 1. if 99 is added t

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Question 820319: the sum of the digits of a number of three digits is 18. if the number is divided by the sum of the ten's and hundred digits the qoutient is 38 the remainder is 1. if 99 is added to the number the digits will be reversed. find the number
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
the sum of the digits of a number of three digits is 18. 
h+t+u = 18

if the number is divided by the sum of the ten's and hundred digits the quotient is 38 the remainder is 1. 
Dividend = (Quotient)(Divisor) + Remainder

100h+10t+u = 38(t+h) + 1
100h+10t+u = 38t+38h+ 1
 62h-28t+u = 1

if 99 is added to the number the digits will be reversed. 
100h+10t+u + 99 = 100u+10t+h
        99h-99u = -99
            h-u = -1

Solve the system of three equations in three unknowns:

  h+  t+u = 18
62h-28t+u =  1
  h    -u = -1

Get h=4, t=9, u=5, number = 495

Edwin
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