Rudolph gives Dasher and Dancer as many sleigh bells as each already has.

Question

Then Dasher gives Rudolph and Dancer as many sleigh bells as each of them then has.
Finally, Dancer gives Dasher and Rudolph as many sleigh bells as each has.
If at the end, each has 16 sleigh bells, how many sleigh bells did each one have at the beginning?

Answer 1

Just read what it says, and write it down in symbols:

If we start out with
x = Rudolph's bells
y = Dasher's
z = Dancer's

after step 1 we have
x-y-z
2y
2z

After step 2 we have
2(x-y-z) = 2x-2y-2z
2y-(x-y-z+2z) = 3y-x-z
4z

After step 3 we have
4x-4y-4z
6y-2x-2z
4z-(2x-2y-2z+3y-x-z) = 7z-x-y

So, now just solve these three equations to get the original x,y,z

4x-4y-4z = 16
6y-2x-2z = 16
7z-x-y = 16

Answer 2

z=8
y = 14
x = 26