Reversed digits -->10y+x

10y+x=2(10x+y)-1

10y+x=20x+2y-1

Subsitute for y:

10(10-x)+x=20x+2(10-x)-1

Expand:

100-10x+x=20x+20-2x-1

Simplfy:

100-9x=18x+19

27x=81

x=3

y=10-3

y=7

Hence, the 10-digit number is 3 and the one digit number is 7.  The number is 37.

Paul.

 

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