Question 258338
<pre><font size = 4 color = "indigo"><b>

The other tutor's solution is correct, although
he didn't give all the reasons, thus used some 
trial and error. Also his first equation a+n=d
is incorrect since there was a carry of 1.

Let x, y be the numbers "to carry", either 1 or 0

 xy
 dna     
+dan    
----    
 and    

Then adding the three columns:

a + n = d + 10y
y + n + a = n + 10x
x + d + d = a

Simplifying:


a - d + n - 10y = 0
a + y = 10x  
a - 2d = x 

The second equation tells us that x can only be 1,
since a can't be 0, so we have this system of equations.

a -    d + n - 10y =  0
a            +   y = 10       
a -   2d           =  1

Solving for the digits in terms of y:

a = 10 - y
d = 4.5 - .5y
n = -5.5 + 10.5y

Thus y = 1 since, among other reasons, a can't be 10,
and we have:

a=9, d=4, n=5, x=1, y=1

 xy      11 
 dna     459 
+dan    +495
----    ----
 and     954

Edwin</pre>