Question

A three digit number is equal to 17 times the sum of its digits. If 198 is added to the number, the digits are interchange. The addition of first and third digit is 1 less than middle digit. Find the number

Answer 1

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!!!!!!!!!!!!!!