Question

Ethan and Liam had 400 marbles in total. Liam had 26 marbles more than Ethan at first. After Ethan and LIam played a game with Cathy, Ethan had 1/14 as many marbles as Liam. If Ethan lost as many marbles as Liam to Cathy, find the numbers of marbles Ethan lost to Cathy.

Answer 1

Ethan at first --- x
Liam at first ---- x+26

x + x+26 = 400
2x = 374
x = 187

So at first Ethan had 187 and Liam had 213 , for a total of 400

after the game:
Ethan lost x marbles to Liam and x marbles to Cathy

Leaving Ethan with 187-x
Liam with 213+x
and Cathy's number + x

Ethan had 1/14 as many marbles as Liam
----> 187-x = (1/14)(213+x)
2618 - 14x = 213 + x
-15x = -2405
x = 160 1/3 , <----- can't have fractional marbles

I can't find any arithmetic error in my work,
either try to find my error or else the question is bogus.