SOLUTION: A three digit number is equal to 17 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 1 less than mid

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Question 1023878: A three digit number is equal to 17 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 1 less than middle digit. Find the number
Answer by jorel555(1290) About Me  (Show Source):
You can put this solution on YOUR website!
Let x,y,and z be the digits:
100x+10y+z=17(x+y+z)
100x+10y+z+198=100z+10y+x
x+z+1=y;
So:
100x+z+198=100z+x
99x+198=99z
x+2=z
x+(x+2)+1=y
y=2x+3
100(x)+10(2x+3)+(x+2)=17(x+2x+3+x+2)
100x+20x+30+x+2=68x+85
53x+32=85
53x=53
x=1,y=5,z=3!!!!!!!!!!!!!!