How to Find the Base in an Equations with Unknown Numbers

[maxfails]

How would you solve a problem like this where you have to find what base A is for this equation to be true? So in what base are these numbers.24)A + 17)A = 40)A

Not asking the answer for this particular question but how you'd solve it (other than trial and error obviously)

 

[rasmhop]

A two digit number ab)A in base A equals $A\cdot a + b$ so:
24)A = 2A + 4
17)A = 1A + 7
40)A = 4A + 0
Then substitute in the equation and solve for A.

 

[zgozvrm]

Simple:

$$24_A = 2*A^1+4*A^0 = 2A + 4$$

Similarly, $$17_A = 1A + 7$$ and $$40_A = 4A + 0$$

Substitute and solve for A