For what base, , is true?

We first translate this into an equation:

\(1*b^1+4*b^0+2*b^1+4*b^0=4*b^1+1*b^0\).

This is equal to \(b+4+2b+4=4b+1\).

Solving we get, \(3b+8=4b+1, b=7\).

Thus, the answer is base \(\boxed{7}.\)

So.....let b be the base.....and we have

(1b + 4)  + ( 2b +4)    = 4b + 1      simplify

3b + 8   = 4b + 1         subtract 3b, 1 from both sides

b = 7

Check

14₇ + 24₇ =  41₇

In base 10

11 + 18  = 29     ⇔   True!!!

Heck.....tertre beat me to it.....LOL!!!