We are out of balance by $92.25. When I add up the digits they total 18 which is divisible by 9, so it could be a transposition error. What possible error could we have made here to arrive at this amount?

Could be anything from a math error on the balance of an account to an error in bringing the balance of an account to a trial balance.

You will have to start with the beginning of your problem and double check your journal entries, your math and the amounts you carry forward to your trial balance if your trial balance is not balancing.

It's not a simple transposition error. If you reverse two digits that are adjacent to each other the error is a multiple of 9 times the difference of the two digits times 10 raised to a power. Since the difference between the two digits ranges from 1 to 9, this means that interchanging two adjacent digits leads to an one of the following errors:


9 x 10^n \\
18 x 10^n \\
27 x 10^n \\
36 x 10^n \\
45 x 10^n \\
54 x 10^n \\
63 x 10^n \\
72 x 10^n \\
81 x 10^n


Here the value of 'n' is the order of the lesser digit. Thus we have the following examples:

7421 versus 7412: delta = 9
7421 versus 7241; delta = 180
7421 versus 4721: delta = 2700.

In your case the error is none of the above values, so you didn't transpose adjacent digits.

More generally, if the transposed digits are not adjacent the resulting error is:


(A-B)10^a(10^n-1)


where A and B are the transposed digits (which must be between 0 and 9), 'a' is the order of the lower digit and (a+n) is the order of the higher digit. Thus for the numbers 765432 and 365472, where the digits in the tens and 100 thousands places are swapped, you have A = 7, B= 3, a = 1 and n = 4, and the difference is

(7-3)10^1(10^4-1) = 4 * 99990 = 399960.

Note that the resulting error is divisible by the number 9999, where the number of 9's is determined by how far apart the swapped digits are in the original number (measured in factors of ten).

So for your case: you have an error of 9225, which is divisible by 9 but the result is not of the form (A-B)10^n, so the transposed digits are not adjacent. But it's not divisible by 99 nor 999, so the transposed digits can't be non-adjacent. Consequently the error is not due to transposed digits.