Rael and Ethan had some coins in the ratio of 11:6. Ethan and Sean had some coins in the ratio of 2:1. Rael sold 112 coins to Sean and ended up with half the number of coins Ethan had. How many coins did Sean have in the end?

So, if Sean started out with 3x coins, then

Ethan had 6x
Rael had 11x
Now we know that
11x-112 = 1/2 * 6x
so x = 14
Sean ended up with 42 + 112 = 154 coins