Question

The elves and reindeer are getting ready for a meeting with Santa.

Answer 1

Let $e$ and $r$ be the number of elves and reindeers, respectively.

We know that:

$r+e=14$ (so far 14 of them have arrived)

$4r+2e = 38$(each reindeer has 4 legs and each elf has two)

If we multiply the first equation by 2 we have $2r+2e=28$, and if we subtract this equation from the second we have $2r=10$ which implies $r=5$.

So, there are 5 reindeers and 9 elves (remember that they have to sum up to 14).