[alpertron]

49k+7m+n = 81n+9m+k

48k-2m-80n = 0
24k-m-40n = 0

1<=k<=6
0<=m<=6
1<=n<=6

m must be multiple of gcd(24,40) = 8, so m=0

m = 0 -> 24k-40m = 0 -> k=5, n=3

So the number in base 7 is 503 (248 decimal), which is equal to 305 in base 9.