SOLUTION: the sum of the digits of a three digit number is 19. The hundreds digit is three times the tens digit. The number is 198 more than the number reversed. Find the original number.

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Question 891658: the sum of the digits of a three digit number is 19. The hundreds digit is three times the tens digit. The number is 198 more than the number reversed. Find the original number.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
H - hundreds place digit
T - tens place digit
U - ones place digit
1.H%2BT%2BU=19
2.H=3T
H%2A100%2BT%2A10%2BU=198%2BU%2A100%2BT%2A10%2BH
100H%2BU=100U%2B198%2BH
99H-99U=198
3.H-U=2
Substituting eq. 2 into eq. 1 and eq. 3,
3T%2BT%2BU=19
4.4T%2BU=19
.
.
5.3T-U=2
Add eqs.4 and 5,
4T%2BU%2B3T-U=19%2B2
7T=21
T=3
Then,
4%283%29%2BU=19
U=19-12
U=7
And,
H=3T
H=3%283%29
H=9
The original number is 937.