SOLUTION: The sum of the digits of 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 327316: The sum of the digits of 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 mananth(16946) About Me  (Show Source):
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The sum of the digits of 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.
x = 100's place
y= 10's place
z= units place
..
x+y+z=19......................1
x=3y
x-3y=0........................2
100x+10y+z -198= 100z+10y+x
rearrange the terms
100x-x+10y-10y+z-100z=198
99x-99z=198
divide by 2
x-z=2.........................3
..
Add equation 1 & 3
x+y+z+x-z=19
2x+y=19
but x=3y from equation 2
plug value of x
2*3y+y=21
7y=21
y=3
equation 2 = x-3y=0
plug value of y
x-3*3=0
x=9
..
x+y+z=19
plug value of x&y
9+3+z=19
12+z=19
z=19-12
z=7
The number is 937