Ramon took a collection of colored tiles from a box. Amelia took 14 tiles from his collection and Keiko took half of those remaining. Ramon had 16 tiles left. How many did he start with?

Be X the number of tiles Ramon started with.

X - 14 = Y

Y/2 = 16 ... > Y = 32

X = 32 + 14 = 46

Ramon started with 46 tiles.

From the given, it is stated that after Amelia took 14 out of the box, Ramon took half of those which remained and he had 16 tiles. The number of tiles left after Amelia took hers is equal to twice of 16 which is equal to 32 tiles.

To determine the number of tiles during the start, we can add the 14 tiles from the calculated 32 tiles.

n = 14 tiles + 32 tiles

n = 46 tiles

Answer: 46 tiles