SOLUTION: A three-digit number is 198 less than the number made when its digits are reversed. Twice the sum of the digits is two less than four times the unit digits. The tens digit is seven
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Question 423712: A three-digit number is 198 less than the number made when its digits are reversed. Twice the sum of the digits is two less than four times the unit digits. The tens digit is seven less than twice the hundreds digit. Find the original number.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
A three-digit number is 198 less than the number made when its digits are reversed. Twice the sum of the digits is two less than four times the unit digits. The tens digit is seven less than twice the hundreds digit. Find the original number.
let the digits be x , y, z
The number xyz
...
100x+10y+z=100z+10y+x-198
99x-99z=-198
/99
x-z=-2.....................1
2(x+y+z)=4z-2
/2
x+y+z=2z-1
x+y-z=-1...........................2
y=2x-7
y-2x=-7.............................3
...
substitute x-z =-2 in (2)
-2+y=-1
y=1
Plug value of y in (3)
1-2x=-7
-2x=-6
x=3
z=5
The number is 315
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