Question 36145
Let the 10-digit be x
Let the one digit be y
x+y=10
y=10-x (subsitution)
The original number is 10x+y
Equation:
<pre><b>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.