Find base of numbers in a sum?

Question

is there an easier way to find the base A in the following without essentially brute-forcing it with different conversions until I get the result?

Again, trying to find base A such that the following addition works.

$$ 24)_{A} + 17)_{A} = 40)_{A} $$

Any help is appreciated, thank you

Answer 1

Convert everything to base $10$: \begin{align*} (2A + 4) + (1A + 7) &= (4A + 0) \\ 3A + 11 &= 4A \\ A &= 11 \end{align*}