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
